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Both private sector organizations and governmental health agencies increasingly use illness severity measures to adjust willingness-to-pay thresholds. Three widely discussed methods—absolute shortfall (AS), proportional shortfall (PS), and fair innings (FI)—all use ad hoc adjustments to cost-effectiveness analysis methods and "stair-step" brackets to link illness severity with willingness-to-pay adjustments. We assess how these methods compare with microeconomic expected utility theory-based methods to value health gains. We describe standard cost-effectiveness analysis methods, the basis from which AS, PS, and FI make severity adjustments. We then develop how the Generalized Risk Adjusted Cost Effectiveness (GRACE) model assesses value for differing illness and disability severity. We compare AS, PS, and FI against value as defined by GRACE. AS, PS, and FI have major and unresolved differences between them in how they value various medical interventions. Compared with GRACE, they fail to properly incorporate illness severity or disability. They conflate gains in health-related quality of life and life expectancy incorrectly and confuse the magnitude of treatment gains with value per quality-adjusted life-year. Stair-step methods also introduce important ethical concerns. AS, PS, and FI disagree with each other in major ways, demonstrating that at most, one correctly describes patients' preferences. GRACE offers a coherent alternative, based on neoclassical expected utility microeconomic theory, and can be readily implemented in future analyses. Other approaches that depend on ad hoc ethical statements have yet to be justified using sound axiomatic approaches. • Absolute severity, proportional severity, and fair innings have increasing use, but without clearly developed economic foundations. • The Generalized Risk Adjusted Cost-Effectiveness method provides a theoretically based benchmark, using preferences of representative utility-maximizing individuals, against which to evaluate these alternative severity adjustment methods. • Absolute severity, proportional severity, and fair innings all have major deficits, compared against Generalized Risk Adjusted Cost-Effectiveness methods, including possible overstatement and understatements of value, conflation of total gains with marginal value, and overstatement of life expectancy gains. Stairstep methods risk violating horizontal and vertical equity criteria. Ethical support for these methods remains unclear and incomplete. [ABSTRACT FROM AUTHOR]

We analyze the effect of strategic ambiguity and heterogeneous attitudes towards such ambiguity on optimal mitigation and adaptation. Pessimistic players tend to invest more in mitigation, while optimists favor adaptation. When adaptation is more expensive than mitigation, three types of equilibria can obtain depending on the level and distribution of ambiguity aversion: (i) a mitigation equilibrium, (i i) an adaptation equilibrium and (i i i) a mixed equilibrium with both adaptation and mitigation. The interaction between ambiguity attitudes and wealth distribution plays a crucial role for the aggregate environmental policy: a wealth transfer from pessimistic to optimistic agents increases total mitigation. A similar result applies to the choice of an optimal mitigation subsidy, which is shown to increase in optimism, but decrease following a transfer of income towards the more optimistic players. Finally, we show that under strategic ambiguity, the introduction of a non-binding standard can impact agents' beliefs about their opponents' behavior and as a result lower total equilibrium mitigation. Our results highlight the necessity to consider attitudes towards strategic ambiguity in the design of economic policies targeting climate change. They might also shed some light on the slow rate of convergence of environmental policies across countries. [ABSTRACT FROM AUTHOR]

This paper models the real-time adaptation of utility when individuals have a limited capacity to make fine distinctions. A simple adaptive mechanism is proposed that adapts utility to an arbitrary distribution of rewards in a way that is ultimately optimal, in terms of minimizing the probability of errors. A modified simple mechanism is approximately optimal in terms of maximizing expected utility. The model generates the so-called "hedonic treadmill" and induces a preference for rising consumption. [ABSTRACT FROM AUTHOR]

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In the early days, Fishburn investigated SD from the view of distributions, and we refer this perspective as Fishburn's SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD cannot be directly generalized, because some properties of fractional calculus may not possess a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD for discrete utilities from the view of distributions. We generalize the order of SD by Lizama's fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be directly generalized from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle it for further applications in mathematics and computer science. [ABSTRACT FROM AUTHOR]

The implications and contagion effect of emotion cannot be ignored in rumor spreading. This paper sheds light on how decision makers' (DMs) emotion type and intensity affect rumor spreading. Based on the rank-dependent expected utility (RDEU) and evolutionary game theory (EGT), we construct an evolutionary game model between rumormongers (RMs) and managers (Ms) by considering emotions. We use MATLAB to simulate and reveal the influencing mechanism of DMs' emotion type and intensity on rumor spreading. The results indicate that the DMs' strategy choice is not only affected by their own emotion preference and intensity, but also by the other players in rumor spreading. Moreover, pessimism has a more significant influence than optimism on the stability of the evolutionary game, Ms' emotion is more sensitive to the game results than RMs' emotion and the emotion intensity is proportional to the evolution speed. More significantly, some earthshaking emotional thresholds are found, which can be used to predict RMs' behavior, help Ms gain critical time to deal with rumors, and avoid the Tacitus Trap crisis. Furthermore, the evolution results fall into five categories: risk, opportunity, ideal, security and hostility. The results of this work can benefit Ms' public governance. [ABSTRACT FROM AUTHOR]

I derive the incentive compatible and individually rational mechanism that maximizes the sum of the buyers' ex-ante expected utilities. I also show that this mechanism minimizes the seller's revenue. When payments are required to be non-negative, my mechanism takes the form of an arbitrarily weighted lottery with no participation fees, and the resulting allocation is generally not ex-post efficient. This means that before learning their valuations and if side payments from the seller to the buyers are not allowed, buyers as a group would be better off if they gave up ex-post efficiency in order to avoid positive payments. When transfers are allowed, the optimal mechanism is a standard auction with no reserve price and where the seller's income is redistributed back to the buyers. This mechanism is robust to speculators if a buyer with value 0 never partakes in the redistribution. [ABSTRACT FROM AUTHOR]

The expanding number of assets offers more opportunities for investors but poses new challenges for modern portfolio management (PM). As a central plank of PM, portfolio selection by expected utility maximization (EUM) faces uncontrollable estimation and optimization errors in ultrahigh-dimensional scenarios. Past strategies for high-dimensional PM mainly concern only large-cap companies and select many stocks, making PM impractical. We propose a sample-average-approximation-based portfolio strategy to tackle the difficulties above with cardinality constraints. Our strategy bypasses the estimation of mean and covariance, the Chinese walls in high-dimensional scenarios. Empirical results on S&P 500 and Russell 2000 show that an appropriate number of carefully chosen assets leads to better out-of-sample mean-variance efficiency. On Russell 2000, our best portfolio profits as much as the equally weighted portfolio but reduces the maximum drawdown and the average number of assets by 10% and 90%, respectively. The flexibility and the stability of incorporating factor signals for augmenting out-of-sample performances are also demonstrated. Our strategy balances the tradeoff among the return, the risk, and the number of assets with cardinality constraints. Therefore, we provide a theoretically sound and computationally efficient strategy to make PM practical in the growing global financial market. for this article are available online. [ABSTRACT FROM AUTHOR]

Tolerancing began with the notion of limits imposed on the dimensions of realized parts both to maintain functional geometric dimensionality and to enable cost-effective part fabrication and inspection. Increasingly, however, component fabrication depends on more than part geometry as many parts are fabricated as a result of a "recipe" rather than dimensional instructions for material addition or removal. Referred to as process tolerancing, this is the case, for example, with IC chips. In the case of tolerance optimization, a typical objective is cost minimization while achieving required functionality or "quality." This article takes a different look at tolerances, suggesting that rather than ensuring merely that parts achieve a desired functionality at minimum cost, a typical underlying goal of the product design is to make money, more is better, and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We further recognize that tolerances introduce additional product attributes that relate to product characteristics such as consistency, quality, reliability, and durability. These important attributes complicate the computation of the expected utility of candidate designs, requiring additional computational steps for their determination. The resulting theory of tolerancing illuminates the assumptions and limitations inherent to Taguchi's loss function. We illustrate the theory using the example of tolerancing for an apple pie, which conveniently demands consideration of tolerances on both quantities and processes, and the interaction among these tolerances. [ABSTRACT FROM AUTHOR]

This paper examines the ordering of economic and financial prospects using a rescaled semivariance below the maximum (SVBMax). This indicator is consistent with stochastic dominance (SD) until order three, but is distinct from any expected utility framework, both in terms of construction and in terms of economic implications, despite an apparent formal similarity with the quadratic expected utility framework. SVBMax is able to deal with economic puzzles such as the restaurant puzzle or Rabin's paradox. SVBMax also provides a consistent alternative performance measure to popular measures such as the Sharpe ratio, the Omega ratio, or lower partial moments with exogenous thresholds. Compared to almost stochastic dominance, SVBMax is devoid of the drawbacks associated with the determination of violation areas. SVBMax can also replace the Aumann-Serrano and Foster-Hart riskiness indicators, which do not conform to third order SD. Further, SVBMax can provide a way of reaching an optimal diversification of stock portfolios. Besides, we also show that SVBMax is consistent with mean-variance-skewness preferences. [ABSTRACT FROM AUTHOR]

In this paper, we consider a non-parametric regression model relying on Riesz estimators. This linear regression model is similar to the usual linear regression model since they both rely on projection operators. We indicate that Riesz estimator regression relies on the positive basis elements of the finite-dimensional sub-lattice generated by the rows of some design matrix. A strong motivation for using the Riesz estimator model is that the data of explanatory variables may come from categorical variables. Calculations related to Riesz estimator regression are very easy since they arise from the measurability in finite-dimensional probability spaces. Moreover, we show that the fitted model of Riesz estimators is an ordinary least squares model. Any vector of some Euclidean space is supposed to be a rendom variable under the objective probability values, being used in expected utility theory and its applications. Finally, the reader may notice that goodness-of-fit measures are similar to those defined for the usual linear regression. Due to the fact that this model is non-parametric, it may include samples relevant to finance and actuarial science variables. [ABSTRACT FROM AUTHOR]

We determined the scope of five decision models of choices across four environmental niches defined by whether outcome probabilities are described (risk) or experienced by sampling (uncertainty) and whether lotteries are simple (one or two outcomes per prospect) or complex (three or four). The majority of participants chose in accordance with cumulative prospect theory only in simple environments involving decisions from description (75%). In complex environments involving decisions from description and experience, however, skewness-preference models were more prevalent (57% and 68%, respectively). Consequently, in niches outside of simple lotteries under risk, rank dependence and nonlinear probability weighting failed to accurately describe the majority of choices. Exploiting elicited subjective beliefs in decisions from experience, we found that experienced (sampled) outcome likelihoods outperformed elicited beliefs in predicting choices and found scant evidence for two-stage models of decisions under uncertainty. Finally, we found statistically significant evidence that 90% of participants chose as if they relied on different models across environments; nonetheless, assuming as if participants used a single model across all environments to predict out-of-sample choice only minimally reduced prediction accuracy. We discuss the implications of model mimicry and task diagnosticity in light of these results in terms of both economic and statistical significance, both for model comparisons and inference. [ABSTRACT FROM AUTHOR]

We improve the traditional simple moving average strategy by incorporating an investor-specific risk tolerance into the method. We then propose a multiasset generalized moving average crossover (MGMA) strategy. The MGMA strategies allocate wealth between risky assets and risk-free assets in an adaptive manner, with the risk tolerance specified by an investor. We derive the expected log-utility of wealth, which allows us to estimate the optimal allocation parameters. The algorithm using our MGMA strategy is also presented. As the multiple risky assets can have different variability levels and could have various degrees of correlations, this trading strategy is evaluated on both simulated data and global high-frequency exchange-traded fund (ETF) data. It is shown that the MGMA strategies could significantly increase both the investor's expected utility of wealth and the investor's expected wealth. [ABSTRACT FROM AUTHOR]

We present a descriptive model of choice derived from neuroscientific models of efficient value representation in the brain. Our basic model, a special case of Expected Utility Theory, can capture a number of behaviors predicted by Prospect Theory. It achieves this with only two parameters: a time-indexed "payoff expectation" (reference point) and a free parameter we call "predisposition". A simple extension of the model outside the domain of Expected Utility also captures the Allais Paradox. Our models shed new light on the computational origins and evolution of risk attitudes and aversion to outcomes below reward expectation (reference point). It delivers novel explanations of the endowment effect, the observed heterogeneity in probability weighting functions, and the Allais Paradox, all with fewer parameters and higher descriptive accuracy than Prospect Theory. [ABSTRACT FROM AUTHOR]

This paper characterizes expected utility preferences with information acquisition and Bayesian updating using stochastic choice data on acts. This contrasts with research that uses state-dependent stochastic choices which is difficult to obtain outside of the laboratory. The characterization is in the spirit of the Wald-Pearce lemma and requires that there is no random deviation rule that improves ex-ante expected utility for all possible information structures consistent with the data. The result is extended to place bounds on an unknown prior and facilitate welfare comparisons in the presence of framing. These bounds are computable via linear programming. Moreover, we show that in special cases, the bounds can be found explicitly by solving a series of Bayesian persuasion games. [ABSTRACT FROM AUTHOR]

Purpose: This study assesses the potential impact of the European Income Stabilization Tool (IST – a whole farm income risk management [RM] tool) within a farm cooperative specializing in vineyards and operating in a small area of production. The authors assess the conditions under which IST could improve the well-being of the associated farmers and, at the same time, improve financial sustainability. Financial aspects are of particular relevance since the characteristics of the cooperative cause the management of the tool to become potentially risky. Design/methodology/approach: The analysis relies on a balanced panel dataset to report the production and economic characteristics of individual associated farms. This is the basis for simulating the implementation of the IST as described in the current European regulation. The expected utility approach is then used to assess the potential impact on farmers' well-being under different levels of risk aversion and premiums. The analysis of the IST annual cash flow allows for an accurate assessment of its financial sustainability. Findings: The results suggest that the IST can improve farmers' well-being under plausible levels of risk aversion and premiums, making most farmers willing to support its implementation. Furthermore, the tool could be financially sustainable even if implemented in a specialized and geographically concentrated group of farms. In addition, the results suggest that the use of strategies such as the IST could help cope with negative annual balances by treating the financial sustainability of the fund. Originality/value: The analysis adds to previous research on the IST by accounting for farmers' risk aversion. Furthermore, it is the first analysis that simulates the implementation of this tool in a sector-specific and concentrated group of farms. The results provide useful evidence for those subjects planning to implement the IST in small and specialized farming systems. [ABSTRACT FROM AUTHOR]

Purpose: The authors investigate whether an index-based weather insurance (WII) product can complement or replace existing traditional crop yield insurance for mitigating farmers' financial risks, with an application to blueberry growers in British Columbia (BC). Design/methodology/approach: A hybrid model combining expected utility (EU) and prospect values is developed to analyse farmers' demand for WII. Findings: While weather data are used to investigate supply elements, a hybrid model combining EU theory and prospect theory (PT) is developed to analyse farmers' demand for WII. On the supply side, a quality index is constructed and the relationship between the quality index and key weather parameters is quantified using a partial least squares structural model. The authors then model weather parameters via time-series analysis and statistical distributions to provide reasonable estimates for calculating actuarially sound insurance premiums for a rainfall indexed, insurance product. This model indicates that decreases in the proportion of a blueberry grower's total revenue and revenue volatility will decrease the possibility that they participate in WII. At the same time, an increase in the value loss aversion coefficient and WII's basis risk further leads to less demand for WII. In short, a grower may decide not to participate in WII at an actuarially fair premium due to the combined effects of the above factors. Overall, while the supply analysis enables us to demonstrate that WII can potentially help in mitigating farmers' financial risks, it turns out that, on the demand side, blueberry growers are unwilling to pay for such a product without large government subsidies. Originality/value: The authors argue that the demand for insurance may be affected by the level and the volatility of a berry grower's total revenue. Hence, the authors propose a hybrid expression that assumes a farmer seeks to maximize the total utility function to capture the rational and intuitive parts of a farmer's decision-making process. The EU represents rationality and the prospect value represents the intuitive component. Meanwhile, the authors investigate the possibility of using key weather parameters to construct a berry quality index – one that could be applied to other agricultural areas for studying the relationship between weather conditions and product quality. [ABSTRACT FROM AUTHOR]

The operational decision-making of low-carbon supply chains with different market structures is studied under the conditions of monopoly and duopoly competition. Considering that the uncertainty about investment in emission reduction technology innovation will lead to disappointment aversion among manufacturers. The constructing corresponding game models are constructed in both cases, and the relevant decision-making issues such as the investment level in emission reduction technologies and pricing of the low-carbon supply chains are discussed. The results show that in a monopoly situation, the investment level in emission reduction technologies, and the manufacturer utility are all negatively related to the disappointment aversion coefficient, and positively related to the investment cost efficiency of emission reduction technologies. In a competitive situation, whether low-carbon manufacturers dominate or both parties have equal power, equilibrium results are negatively related to the disappointment aversion coefficient, and positively related to the unit travel cost of consumers, retail price of low-carbon products are higher when low-carbon manufacturers dominate than that when power is equal; the investment level in emission reduction technologies when low-carbon manufacturers are dominant is lower than that when the powers of the two parties are equal, and in all power structures, the expected profit and utility of low-carbon manufacturers are negatively related to the investment cost coefficient in emission reduction technologies, while ordinary manufacturers are on the contrary. [ABSTRACT FROM AUTHOR]

Many practical decisions are more realistic concerning preventing bad decisions than seeking better ones. However, there has been no behavioral decision theory research on avoiding the worst decisions. This study is the first behavioral decision research on decision strategies from the perspective of avoiding the worst decisions. We conducted a computer simulation with the Mersenne Twister method and a psychological experiment using the monitoring information acquisition method for two-stage decision strategies of all combinations for different decision strategies: lexicographic, lexicographic semi-order, elimination by aspect, conjunctive, disjunctive, weighted additive, equally weighted additive, additive difference, and a majority of confirming dimensions. The rate of choosing the least expected utility value among the alternatives was computed as the rate of choosing the worst alternative in each condition. The results suggest that attention-based decision rules such as disjunctive strategy lead to a worse decision, and that striving to make the best choice can conversely often lead to the worst outcome. From the simulation and the experiment, we concluded that simple decision strategies such as considering what is most important can lead to avoiding the worst decisions. The findings of this study provide practical implications for decision support in emergency situations. [ABSTRACT FROM AUTHOR]

The decision to transfer or share an insurable risk is critical for the decision maker's economy. This paper deals with this decision, starting with the definition of a function that represents the difference between the expected utility of insuring, with or without deductibles, and the expected utility of not insuring. Considering a constant relative risk aversion (CRRA) utility function, we provide a decision pattern for the potential policyholders as a function of their wealth level. The obtained rule applies to any premium principle, any per-claim deductible and any risk distribution. Furthermore, numerical results are presented based on the mean principle, a per-claim absolute deductible and a Poisson-exponential model, and a sensitivity analysis regarding the deductible parameter and the insurer security loading was performed. One of the main conclusions of the paper is that the initial level of wealth is the main variable that determines the decision to insure or not to insure; thus, for high levels of wealth, the decision is always not to insure regardless of the risk aversion of the decision maker. Moreover, the parameters defining the deductible and the premium only have an influence at low levels of wealth. [ABSTRACT FROM AUTHOR]

In view of the random retail price and retailer's preference for retail price risk aversion, we used mean-variance to describe the uncertainty risk of retail price. To study the impacts of both the retail price uncertainty risk and retail price risk aversion preference on supply chain (SC) decision-making, we constructed a SC game model based on three different power structures, including Manufacturer Stackelberg (MS) game, Retailer Stackelberg (RS) game, and Vertical Nash (VN) game. The results showed that the retail price uncertainty risk and the retailer's retail price risk aversion preference weakened the manufacturer's production effort input, decreased the retailer's enthusiasm for ordering, and damaged the interests of manufacturer and retailer. Under the three different power structures, the production effort input of the manufacturer depended on the production effort affecting wholesale price efficiency and retail price efficiency. The retailer's expected utility was largest under the MS game model and smallest under the VN game model. The manufacturer's profits were closely related to each parameter under the three respective power structures. This study provides theoretical guidance for the decision-making of SC enterprises with retail price risk and retailer with retail price risk aversion preference under different power structure situations. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has brought health systems to the brink of collapse in several regions around the world, as the demand for health care has outstripped the capacity of their services, especially regarding intensive care. In this context, health system managers have faced a difficult question: who should be admitted to an intensive care unit (ICU), and who should not? This paper addresses this decision problem using Expected Utility Theory and Bayesian decision analysis. In order to estimate the chances of survival for patients, a structured protocol has been proposed conjointly with physicians, based on the Sequential Organ Failure Assessment (SOFA) score. A portfolio selection approach is proposed to support tackling the ICU allocation problem. A simulation study shows that the proposed approach is more advantageous than other approaches already presented in the literature, with respect to the number of lives saved. The patients' probabilities of survival inside and outside the ICU are important parameters of the model. However, assessing such probabilities can be a difficult task for health professionals. In order to give due treatment to the imprecise information regarding these probabilities, a Monte Carlo simulation is used to estimate the probabilities of recommending a patient be admitted to the ICU is the most appropriate decision, given the conditions presented. The methodology was implemented in an Information and Decision System called SIDTriagem, which is available online for free. With regards to managerial implications, SIDTriagem has a great potential to help in the response to public health emergencies systems as it facilitates rational decision-making regarding allocating ICU beds when resources are scarce. [ABSTRACT FROM AUTHOR]

This paper considers a dynamic Stackelberg game model for a manufacturer-led supply chain with risk aversion. Cooperative advertising strategy is applied to the marketing decisions of supply chain participants. Based on Stackelberg game and system dynamic theory, the game and complex dynamical behaviors are studied through the use of several methods, such as the stability region of the system, bifurcation diagram, attractor diagram, and the largest Lyapunov exponent diagram. The expected utilities of participants are given and compared by numerical simulation. The results illustrate that a series of variations in adjustment speed of advertising expenditure, participation rate of local advertising expenditure by manufacturer, risk tolerance levels, and the effect coefficient of advertising expenditure may cause a loss of stability to the system and evolve into chaos. Meanwhile, the Nash equilibrium point and the expected utility of the manufacturer and retailer will change greatly. The parameter control method is further applied to control the chaos phenomenon of the system effectively. By means of analyzing the impact of relevant factors on the game model, the manufacturer and retailer can make optimal strategy decisions in the supply chain competition. The findings of this study mainly include the following three aspects. Firstly, for market stability and maximizing revenue, the manufacturer adjusts the participation rate appropriately, avoiding too high or too low values. Secondly, the manufacturer will try to reduce their own risk tolerance level for the economic revenue, and the retailer appropriately adjust the risk tolerance level to adapt to their own development according to their own enterprise strategy. Finally, both the manufacturer and retailer reduce their own effect coefficients of advertising expenditure. Meanwhile, they will attempt to increase their opponent's effect coefficient to gain the most revenue. The research results of this study can provide important reference for the advertising expenditure decision and revenue maximization of participants in the context of risk aversion. [ABSTRACT FROM AUTHOR]

We study a cyber security game between a defender who wishes to defend her information assets and an attacker who tries to attack them. In this game the attacker and the defender choose how to distribute their resources in attacking or defending the different information assets. Given these investments the probability that an attack on a given asset is successful is an increasing function of the attacker's investment and a decreasing function of the defender's investment. The defender tries to minimize the expected damage from the attacks plus the cost of the defense while the attacker tries to maximize the expected damage from attacks minus his attacks' expenses. The attacker is constrained by a budget. We compare two scenarios: a sequential move game and a simultaneous game. In the sequential game the defender moves first by deciding how much resources to allocate to the defense of each information asset and the attacker observes these investments and responds by allocating his resources in a manner that maximizes his expected utility. In the simultaneous game the attacker does not observe the defender's decision before making his own. We analyze the best response strategies of the players and the equilibria of each of these games. Based on this analysis, we provide a tight upper bound on the reduction in defender's costs that can be achieved by moving from the simultaneous to the sequential game. [ABSTRACT FROM AUTHOR]

A company with $n$ geographically widely dispersed sites seeks insurance that pays off if $m$ out of the $n$ sites experience rarely occurring catastrophes (e.g., earthquakes) during a year. This study describes an adaptive dynamic strategy that enables an insurance company to offer the policy with smaller loss probability than more conventional static policies induce, but at a comparable or lower premium. The strategy accomplishes this by periodically purchasing reinsurance on individual sites. Exploiting rarity, the policy induces zero loss with probability one if no more than one quake occurs during any review interval. The policy also may induce a profit if $m$ or more quakes occur in an interval if no quakes have occurred in previous intervals. The study also examines the benefit of more than one reinsurance policy per active site. The study relies on expected utility to determine indifference premiums and derives an upper bound on loss probability independent of premium. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean–variance criterion controlling the final risk of the portfolio. The multiple-objective optimization problem is firstly transformed into a single-objective one by introducing the concept of overall 'happiness' of an investor defined as the aggregation of the terminal wealth under the mean–variance criterion and the expected accumulated utility, and then solved under a game-theoretic framework. We have managed to maintain analytical tractability; the closed-form solutions found for a set of special utility functions enable us to discuss some interesting optimal investment strategies that have not been revealed in the literature before. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of excess-of-loss reinsurance and investment for an insurer who wishes to maximize the expected exponential utility of the terminal wealth. The surplus process of the insurer is described by a Brownian motion with drift, while the claim arrival process, the insurance and reinsurance premiums are affected by a stochastic factor. It is also assumed that the risky asset in the financial market have time varying and random coefficients. By applying the Hamilton-Jacobi-Bellman (HJB) equation approach, both the value function and the corresponding optimal strategies are obtained and characterized under different premium calculation principles. Furthermore, the existence and uniqueness of the solution to the HJB equation is also discussed. Finally, numerical examples are presented to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper studies the optimal investment-consumption decision under the constant elasticity of variance (CEV) model for an individual seeking to maximize the expected utility from cumulative consumption plus the expected utility from terminal wealth. Due to the fact that different individuals may have different risk preferences, we assume that the risk preference of an individual satisfies a hyperbolic absolute risk aversion (HARA) utility function. Generally speaking, power utility function, logarithmic utility function and exponential utility function widely used in investment theory are usually special cases of HARA utility function. By using the principle of dynamic programming and Legendre transform-dual technique, we obtain the explicit expression of the optimal investment-consumption decision. In addition, we derive the results under other utility functions as well and analyze some characteristics of the optimal portfolios and the optimal consumption decisions. A numerical simulation is presented to illustrate our results. Research results suggest that the optimal investment decisions between with consumption behavior and without it have considerable differences. [ABSTRACT FROM AUTHOR]

We consider a two-level supply chain comprising a retailer and capital-constrained farmer, with three cases of behavioural preferences: stockout aversion (SA), waste aversion (WA), and stockout and waste aversion (SW); the farmer can solve financial constraints through bank loans and internal financing. We analyse the financing decision simulation of the farmer in a yield uncertain environment. The results show that – regardless of the preferences of the farmer – the largest expected utility and production input of the farmer and the expected profit and order quantity of the retailer are those under internal financing, followed by bank loans and non-financing. Finally, we analyse the influence of the farmer's SA and WA on the expected utility (profit) and decision-making of supply chain members by numerical simulation. Most supply chain studies do not factor in the high risk faced by farmers. Our study provides data on various option outcomes for those advising farmers facing difficult financing decisions. [ABSTRACT FROM AUTHOR]

We introduce a new fairness measure for designing organ allocation rules for transplantation. In particular, we apply the proportional fairness measure for organ transplantation whose solution can be interpreted as the solution to the Nash bargaining problem for sharing limited donor organs among patients who seek to maximize their Quality-Adjusted Life-Years (QALYs). The motivation arises from several observations that current measures of fairness induce significant inefficiencies in terms of total QALYs of the patient population. We use the asymptotic results for the fluid approximation of a transplant queuing system to estimate the expected utility of patients and formulate an optimization problem where the decision maker partitions the set of organ types to achieve a proportionally fair objective. We use an achievable region approach to transform our formulation to an alternative optimization problem and show that the optimal allocation policy under the proportional fairness measure is assortative, which has the following insight: higher quality organs are allocated to patients who will have higher expected QALYs. We compare the performance of allocation rules developed for fairness purposes in organ allocation along with our proposed policy via a validated simulation model for heart transplantation in the US. [ABSTRACT FROM AUTHOR]

We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for generic market dynamics given by a subclass of multidimensional Itô processes we specify and prove the equivalence between No-Free-Lunch-with-Vanishing-Risk (NFLVR) and expected utility maximization. As a by-product, we provide a geometric characterization of the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition given by the zero curvature (ZC) condition for this subclass of Itô processes. Finally, we extend the Black–Scholes partial differential equation to markets allowing arbitrage. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal reinsurance problem for a risk model with a thinning-dependence structure, where the stochastic sources related to claim occurrence are classified into different groups, and each group may cause a claim in each insurance class with some probability. We assume that the insurer can manage the risk by purchasing per-loss reinsurance, and their aim is to maximize the expected utility of the terminal wealth. By using the technique of stochastic control, we obtain the corresponding Hamilton–Jaccobi–Bellman equation. From the perspective of game theory, we derive the closed-form expression of the optimal strategy for each class of business, which is actually the best response to other given strategies. We also investigate the necessary conditions for optimal strategies and transfer the original optimization problem into a system of equations. Furthermore, we prove that the solution of the system of equations always exists, but may not be unique, and we also study some features of the optimal strategies in special cases and derive several interesting results. Finally, some numerical examples are given to show the impacts of some important parameters on the optimal strategies. [ABSTRACT FROM AUTHOR]

This paper considers an observable double-ended queueing system of passengers and taxis, where matching times follow an exponential distribution. We assume that passengers are strategic and decide to join the queue only if their expected utility is nonnegative. We show that the strategy of passengers is represented by a unique vector of thresholds corresponding to different cases of the number of taxis observed in the system upon passenger arrival. Furthermore, we develop a heuristic algorithm to find an optimal range of fees to be levied on passengers to maximize social welfare or revenues. [ABSTRACT FROM AUTHOR]

This study examines the effects of supply reliability, risk aversion, and wealth on the optimal order strategy of retailers in the case of uncertain demand by measuring the degree of risk aversion. A more practical model of optimal ordering strategy is proposed, considering supply reliability, demand uncertainty, risk aversion, and retailer wealth, in which two random variables, supply reliability factors and demand, are introduced into the retailer's function of expected utility. To avoid nonconvergence at both ends, the demand follows a triangular rather than a normal distribution. It is found that the optimal order quantity will increase with the improvement of supply reliability when the risk-averse degree is fixed. The results also show that the optimal order quantity of risk-averse retailers is smaller than that of risk-neutral retailers. Additionally, the optimal order quantity for the risk-averse retailer decreases as the degree of risk aversion increases, when supply reliability is fixed. Further research shows that the retailer is a constant absolute risk aversion (CARA). That means retailer's wealth has nothing to do with the risk aversion and changes in the retailer's wealth will not affect the retailer's optimal order quantity. This study provides valuable insights for sustainable supply chain management and marketing. [ABSTRACT FROM AUTHOR]

How do people make everyday decisions in order to achieve the most successful outcome? Decision making research typically evaluates choices according to their expected utility. However, this research largely focuses on abstract or hypothetical tasks and rarely investigates whether the outcome is successful and satisfying for the decision maker. Instead, we use an everyday decision making task inwhich participants describe a personally meaningful decision they are currently facing. We investigate the decision processes used to make this decision, and evaluate how successful and satisfying the outcome of the decision is for them. We examine how well analytic, attribute-based processes explain everyday decision making and predict decision outcomes, and we compare these processes to associative processes elicited through free association. We also examine the characteristics of decisions and individuals that are associated with good decision outcomes. Across three experiments we found that: 1) an analytic decision analysis of everyday decisions is not superior to simpler attribute-based processes in predicting decision outcomes; 2) contrary to research linking associative cognition to biases, free association generates valid cues that predict choice and decision outcomes as effectively as attribute-based approaches; 3) contrary to research favouring either attribute-based or associative processes, combining both attribute-based and associates best explains everyday decisions and most accurately predicts decision outcomes; and 4) individuals with a tendency to attempt analytic thinking do not make more successful everyday decisions. Instead, frequency, simplicity, and knowledge of the decision predict success. We propose that attribute-based and associative processes, in combination, both explain everyday decision making and predict successful decision outcomes. [ABSTRACT FROM AUTHOR]

The goal of a sequential decision-making problem is to design an interactive policy that adaptively selects a group of items, each selection is based on the feedback from the past, to maximize the expected utility of selected items. It has been shown that the utility functions of many real-world applications are adaptive submodular. However, most of existing studies on adaptive submodular optimization focus on the average-case, that is, their objective is to find a policy that maximizes the expected utility over a known distribution of realizations. Unfortunately, a policy that has a good average-case performance may have very poor performance under the worst-case realization. In this study, we propose to study two variants of adaptive submodular optimization problems, namely, worst-case adaptive submodular maximization and robust submodular maximization. The first problem aims to find a policy that maximizes the worst-case utility and the latter one aims to find a policy, if any, that achieves both near optimal average-case utility and worst-case utility simultaneously. We introduce a new class of stochastic functions, called worst-case submodular function. For the worst-case adaptive submodular maximization problem subject to a p-system constraint, we develop an adaptive worst-case greedy policy that achieves a 1 p + 1 approximation ratio against the optimal worst-case utility if the utility function is worst-case submodular. For the robust adaptive submodular maximization problem subject to cardinality constraints (respectively, partition matroid constraints), if the utility function is both worst-case submodular and adaptive submodular, we develop a hybrid adaptive policy that achieves an approximation close to 1 − e − 1 2 (respectively, 1/3) under both worst- and average-case settings simultaneously. We also describe several applications of our theoretical results, including pool-base active learning, stochastic submodular set cover, and adaptive viral marketing. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1239. [ABSTRACT FROM AUTHOR]

We study a discrete-time finite-horizon two-player nonzero-sum stopping game where the filtration of Player 1 is richer than the filtration of Player 2. A major difficulty which is caused by the information asymmetry is that Player 2 may not know whether Player 1 has already stopped the game or not. Furthermore, the classical backward-induction approach is not applicable in the current setup. This is because when the informed player decides not to stop, he reveals information to the uninformed player, and hence the decision of the uninformed player at time t may be determined not only by the play after time t, but also by the play before time t. In the current work we initially show that the expected utility of Player 2 will remain the same even if he knows whether Player 1 has already stopped. Then, this result is applied in order to prove that, under appropriate conditions, a recursive construction in the style of Hamadène and Zhang (2010) converges to a pure-strategy Nash equilibrium. [ABSTRACT FROM AUTHOR]

A number of analytic solutions have been found for Variable Annuity Guaranteed Minimum Death Benefit (GMDB) option values under a variety of mortality laws. To date, the solutions are for Risk-Neutral valuation only. Where policyholder decisions are allowed, it is assumed that they act to maximize the risk-neutral value of the GMDB. We examine situations where the asset allocation decisions are made to maximize expected utility rather than option value. We find analytic solutions for both return of premium and ratchet options at small values of bequest motive for a number of mortality laws. [ABSTRACT FROM AUTHOR]

This paper first studies the optimal reinsurance problems for two competitive insurers and then studies the optimal reinsurance premium pricing problem for their common reinsurer by using the dynamic programming technique. The two insurers are subject to common insurance systematic risk. Each purchases proportional or excess-of-loss reinsurance for risk control. They aim to maximize the expected utilities of their relative terminal wealth. With the insurers' optimal reinsurance strategies, the reinsurer decides the reinsurance premiums for each insurer, also aiming to maximize the expected utility of her terminal wealth. Thus, the optimal reinsurance pricing problem is formulated as a Stackelberg game between two competitive insurers and a reinsurer, where the reinsurer is the leader, and the insurers are followers. Besides, all three players take model ambiguity into account. We characterize the optimal strategies for the insurers and the reinsurer and provide some numerical examples to show the impact of competition and model ambiguity on the pricing of reinsurance contracts. [ABSTRACT FROM AUTHOR]

This paper studies the relation of information cost, retail investor sentiment and asset pricing. Our motivation to study this model is to learn why retail investors could move asset price away from fundamental values. In the model, the institutional investors are pessimistic and the retail investors are optimistic, the ratio of the expected utility of informed and rational but uninformed institutional investors increases first and then decreases as the cost of information increases. In addition, a large number of retail investors promoted substantial increases in stock prices. This model provides part of the explanation for the unusually high stock price of Game Stop in early 2021 that retail investors cliqued and confronted institutional investors. [ABSTRACT FROM AUTHOR]

As an essential problem in robotics, foraging means that robots collect objects from a given environment and return them to a specified location. On many occasions, robots are required to perform foraging tasks in adversarial environments, such as battlefield rescue, where potential adversaries may damage robots with a certain probability. The longer an individual robot moves through adversarial environments, the higher the probability of being damaged by adversaries. The robot system can gain utility only when the robot brings carried objects back to a predetermined home station. Such a risk of being damaged makes returning home at different locations potentially relevant to the expected utility produced by the robot. Thus, the individual robot faces a dilemma when it responds to the potential risks in adversarial environments: whether to return the carried resources home or continue foraging tasks. In this article, two fundamental environment settings are discussed, homogeneous cases and heterogeneous cases. The former is analyzed as having both the optimal substructure property and the non-aftereffect property. Then, we present a dynamic programming (DP) algorithm that can find an optimal solution with polynomial time complexity. For the latter, it is proven that finding an optimal solution is \(\mathcal {NP} \) -hard. We then propose a heuristic algorithm: A division hierarchical path planning (DHPP) algorithm that is based on the idea of dividing the foraging routes generated initially into a certain number of subroutes to dilute risks. Finally, these algorithms are extensively evaluated in simulations, concluding that in adversarial environments, they can significantly improve the productivity of an individual robot before it is damaged. [ABSTRACT FROM AUTHOR]

We use a model of impressionable voters to study multi-candidate elections under different electoral rules. Instead of maximizing expected utility, voters cast their ballots based on impressions. We show that, under each rule, there is a monotone relationship between voter preferences and vote measures. The nature of this relationship, however, varies by electoral rule. Vote measures are biased upwards for socially preferred candidates under plurality rule, but biased downwards under negative plurality. There is no such bias under approval voting or Borda count. Voters always elect the socially preferred candidate in two-way races for any electoral rule. In multi-candidate elections, however, the ability to elect a Condorcet winner varies by rule. The results show that multi-candidate elections can perform well even if voters follow simple behavioral rules. The relative performance of specific electoral institutions, however, depends on the assumed behavioral model of voting. [ABSTRACT FROM AUTHOR]

Ben-Tal and Teboulle [Management Sci., 32 (1986), pp. 1445--1466] introduce the concept of optimized certainty equivalent (OCE) of an uncertain outcome as the maximum present value of a combination of the cash to be taken out from the uncertain income at present and the expected utility value of the remaining uncertain income. In this paper, we consider two variations of the OCE. First, we introduce a modified OCE by maximizing the combination of the utility of the cash and the expected utility of the remaining uncertain income so that the combined quantity is in a unified utility value. Second, we consider a situation where the true utility function is unknown but it is possible to use partially available information to construct a set of plausible utility functions. To mitigate the risk arising from the ambiguity, we introduce a robust model where the modified OCE is based on the worst-case utility function from the ambiguity set. In the case when the ambiguity set of utility functions is constructed by a Kantorovich ball centered at a nominal utility function, we show how the modified OCE and the corresponding worst-case utility function can be identified by solving two linear programs alternatively. We also show that the robust modified OCE is statistically robust in a data-driven environment where the underlying data are potentially contaminated. Some preliminary numerical results are reported to demonstrate the performance of the modified OCE and the robust modified OCE model. [ABSTRACT FROM AUTHOR]

Yaari's dual theory of choice under risk is the natural counterpart of expected utility theory. While optimal payoff choice for an expected utility maximizer is well studied in the literature, less is known about the optimal payoff for a Yaari investor. We perform a fairly general analysis and derive optimal payoffs in a variety of relevant cases. As a main contribution, we provide the optimal payoff for a Yaari investor under a variance constraint; thus, extending mean–variance optimization to distorted expectation–variance optimization. We also derive the optimal payoff for an investor who aims to outperform an external benchmark under the requirement that the payoff stays in the neighbourhood of this benchmark. [ABSTRACT FROM AUTHOR]

Many farmers hesitate to adopt new management strategies with actual or perceived risks and uncertainties. Especially in ornamental plant production, farmers often stick to current production strategies to avoid the risk of economically harmful plant losses, even though they may recognize the need to optimize farm management. This work focused on the economically important and little-researched production system of ornamental heather (Calluna vulgaris) to help farmers find appropriate measures to sustainably improve resource use, plant quality, and profitability despite existing risks. Probabilistic cost-benefit analysis was applied to simulate alternative disease monitoring strategies. The outcomes for more intensive visual monitoring, as well as sensor-based monitoring using hyperspectral imaging were simulated. Based on the results of the probabilistic cost-benefit analysis, the expected utility of the alternative strategies was assessed as a function of the farmer's level of risk aversion. The analysis of expected utility indicated that heather production is generally risky. Concerning the alternative strategies, more intensive visual monitoring provides the highest utility for farmers for almost all levels of risk aversion compared to all other strategies. Results of the probabilistic cost-benefit analysis indicated that more intensive visual monitoring increases net benefits in 68% of the simulated cases. The application of sensor-based monitoring leads to negative economic outcomes in 85% of the simulated cases. This research approach is widely applicable to predict the impacts of new management strategies in precision agriculture. The methodology can be used to provide farmers in other data-scarce production systems with concrete recommendations that account for uncertainties and risks. [ABSTRACT FROM AUTHOR]

In the face of increasingly complex market environment, supply chain members pay attention to the possibility of obtaining expected profits and various risks while considering profit maximization. The behaviors of decision makers are often influenced by their psychological preferences, and loss aversion is one of the basic characteristics of human economic behavior. We research the supply chain coordination problem with capital constraint and loss-averse retailer in the case of stochastic production and demand. In order to address the loss aversion, a novel utility function is structured according to the theory of mental account. Under wholesale price contract, the optimal expected utility of supply chain under decentralized decision is smaller than that under centralized decision due to the retailer's constrained capital. Based on that, a model is constructed by making revenue sharing contract act as the dual role of supply chain coordination and delayed payment strategy without seeking external financing or internal financing, and the contract conditions and optimal decisions of the coordinated supply chain are solved. Theoretical analysis indicates that when the contract parameters are properly selected, even though the retailer's capital is constrained, the revenue sharing contract can not only coordinate the supply chain but also realize the arbitrary distribution of supply chain profits within a certain range. Finally, the change of decision variables and expected utility or profit with contract parameters is analyzed by several numerical examples. [ABSTRACT FROM AUTHOR]

Risk aversion, which refers to the reluctant attitude of an economic agent to accept uncertain outcomes compared with a certain one even if the latter has a lower outcome in monetary value, plays a fundamental role in decision theory and risk management. This paper investigates how to measure different agents' risk-averse attitudes towards a risky situation consisting of multiple uncertain components under uncertainty theory. First, a general method to approximately compute the multivariate uncertain risk premium is proposed. Subsequently, the multivariate uncertain risk aversion is formally defined based on the multivariate uncertain risk premium, and the corresponding sufficient condition for utility functions being multivariate risk-averse is given. Its relation to Richard's correlation aversion under the framework of uncertainty theory is also discussed. Finally, the suggested theoretical findings are applied to an accounts receivables (ARs) pricing problem to exhibit their applicability. The results show that our method is more applicable in practice than the univariate approach. Moreover, for the AR financing, the AR owner should choose higher-credit trading partners and financial institutions with less risk aversion to cooperate for acquiring more cash. [ABSTRACT FROM AUTHOR]