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This paper studies the supplier selection and order allocation (SS&OA) problem, where risks include a series of disruption scenarios with uncertain probability of occurrence. It is a challenge for industry decision-makers to balance the average cost and the level of risk under the ambiguity set for probabilities. To address this challenge, a two-stage distributionally robust (DR) Mean-CVaR model is presented for the SS&OA problem. A procedure is developed for constructing the ambiguity set, and Polyhedral and Box ambiguity sets are constructed to characterise the uncertain probabilities. The worst-case Mean-CVaR criterion is employed for the second-stage cost within the ambiguity set to trade off the expected cost and CVaR value. Three measures are incorporated to increase the resilience of the supply chain. The proposed robust model is reformulated into two mixed-integer linear programming models. A real case of the Huawei cell phone manufacturer is used to illustrate the validity of the proposed approach in numerical settings. Experimental results show that the new optimising approach can provide a robust SS&OA solution to immunise against the influence caused by uncertain probabilities. By comparative analyses, some management insights are obtained for industry decision-makers. [ABSTRACT FROM AUTHOR]

Nonlinear dependence on a probability measure has recently been encountered with increasing intensity in stochastic optimization. This type of dependence corresponds to many situations in applications; it can appear in problems static (one-stage), dynamic with finite (multi-stage) or infinite horizon, and single- and multi-objective ones. Moreover, the nonlinear dependence can appear not only in the objective functions but also in the constraint sets. In this paper, we will consider static one-objective problems in which the nonlinear dependence appears in the objective function and may also appear in the constraint sets. In detail, we consider "deterministic" constraint sets, whose dependence on the probability measure is nonlinear, constraint sets determined by second-order stochastic dominance, and sets given by mean-risk problems. The last mentioned instance means that the constraint set corresponds to solutions which guarantee acceptable values of both criteria. To obtain relevant assertions, we employ the stability results given by the Wasserstein metric, based on the L 1 norm. We mainly focus on the case in which a solution has to be obtained on the basis of the data and of investigating a relationship between the original problem and its empirical version. [ABSTRACT FROM AUTHOR]

We consider the problem of finding (Pareto-)optimal allocations of risk among finitely many agents. The associated individual risk measures are law-invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, we assume that the individual risk assessments are consistent with the respective second-order stochastic dominance relations, but remain agnostic about their convexity. A simple sufficient condition for the existence of Pareto optima is provided. The proof combines local comonotonic improvement with a Dieudonné-type argument, which also establishes a link of the optimal allocation problem to the realm of "collapse to the mean" results. [ABSTRACT FROM AUTHOR]

Recent trends in portfolio management emphasize the importance of reducing carbon footprints and aligning investments with sustainable practices. This paper introduces Sensitivity Value-at-Risk (SensitivityVaR), an advanced distortion risk measure that combines Value-at-Risk (VaR) and Expected Shortfall (ES) with the Cornish–Fisher expansion. SensitivityVaR provides a more robust framework for managing risk, particularly under extreme market conditions. By incorporating first- and second-order distorted stochastic dominance criteria, we enhance portfolio decarbonization strategies, aligning financial objectives with environmental targets such as the Paris Agreement's goal of a 7% annual reduction in carbon intensity from 2019 to 2050. Our empirical analysis evaluates the impact of integrating carbon intensity data—including Scope 1, Scope 2, and Scope 3 emissions—on portfolio optimization, focusing on key sectors like technology, energy, and consumer goods. The results demonstrate the effectiveness of SensitivityVaR in managing both risk and environmental impact. The methodology led to significant reductions in carbon intensity across different portfolio configurations, while preserving competitive risk-adjusted returns. By optimizing tail risks and limiting exposure to carbon-intensive assets, this approach produced more balanced and efficient portfolios that aligned with both financial and sustainability goals. These findings offer valuable insights for institutional investors and asset managers aiming to integrate climate considerations into their investment strategies without compromising financial performance. [ABSTRACT FROM AUTHOR]

This article extends the socially responsible multiobjective problem to (i) estimating optimal portfolios via reward/risk maximization, (ii) including dependence structure between asset returns using vine copulas, and (iii) incorporating enhanced indexation utilizing cumulative zero-order stochastic dominance (CZϵSD). Applying the multiobjective optimal portfolio (MOOP) approach to a sample of EuroStoxx 50 constituents, the results show that the MOOPs provide investors with the flexibility to incorporate different objectives while investing in optimal portfolios. Including social responsibility results in lower portfolio return and economic performance, but at the same time portfolio risk, expected shortfall of portfolio returns below the benchmark, and turnover are reduced. The copula-based predictive models lead to MOOPs with higher returns and reward/risk ratios. Moreover, optimizing environmental scores leads to less risky MOOPs, while optimizing social scores results in higher average return and better risk-adjusted performance. [ABSTRACT FROM AUTHOR]

Ungulate herbivores shape grassland plant communities at multiple scales, ultimately affecting ecosystem function. However, ungulates have complex effects on grasslands, including defoliation, trampling, excreta return and their interactions. Moreover, the effects of ungulate density on grasslands are regulated by these three mechanisms. Nevertheless, how these three mechanisms affect biodiversity at multiple scales and community assembly remains poorly understood.Here, we conducted a 4‐year novel field experiment to disentangle the effects of defoliation, trampling, and excreta return by ungulates on plant community assembly in a temperate grassland in Inner Mongolia, China. This experiment set two different scenarios: moderate ungulate density (Moderate, characterised by selective defoliation and moderate trampling) and high ungulate density (Intense, characterised by non‐selective defoliation and heavy trampling), including different combinations of defoliation, trampling and excreta return in each scenario.We found that defoliation and trampling increased stochasticity in community assembly and promoted alpha and beta diversity under both scenarios. Specifically, defoliation promoted the coexistence of species with multiple resource acquisition strategies (higher functional trait diversity) by reducing interspecific competition; trampling tended to facilitate random species colonisation. Conversely, excreta return favoured grasses, promoting deterministic assembly and impacting species coexistence. Notably, selective defoliation in the Moderate scenario led to a dominance of stochastic processes during community assembly, whereas non‐selective defoliation still did not change the dominance of deterministic processes. Further, communities subject to selective defoliation were insensitive to changes in soil properties caused by trampling and excreta return, maintaining a high‐level beta diversity and the stochastic of community assembly.Synthesis: Our study provides important insights into the mechanisms by which ungulate herbivores influence plant community assembly, suggesting that defoliation and trampling have the potential to drive stochastic processes, while excreta return plays the opposite role. Our study also suggests that selective foraging by ungulates acts as stronger stochastic forces during community assembly compared to non‐selective defoliation. These results imply that considering ungulate feeding preferences and foraging behaviour in grassland management will help prevent biodiversity loss and biotic homogenisation. [ABSTRACT FROM AUTHOR]

A 2022 paper [7] introduced the notion of true positive and negative skewness for continuous random variables via Fréchet -means. In this work, we find novel criteria for true skewness and establish true skewness for the Weibull, Lévy, and skew-normal distributions. Furthermore, some relevant properties of the -means of random variables are established. [ABSTRACT FROM AUTHOR]

Problem definition: In this paper, we study the newsvendor problem under some distributional ambiguity sets and explore their relations. Additionally, we explore the benefits of implementing this robust solution in the feature-based newsvendor problem. Methodology and results: We propose a new type of discrepancy-based ambiguity set, the JW ambiguity set, and analyze it within the framework of first-order stochastic dominance. We show that the distributionally robust optimization (DRO) problem with this ambiguity set admits a closed-form solution for the newsvendor loss. This result also implies that the newsvendor problem under the well-known infinity-Wasserstein ambiguity set and Lévy ball ambiguity set admit closed-form inventory levels as a by-product. In the application of feature-based newsvendor, we adopt general kernel methods to estimate the conditional demand distribution and apply our proposed DRO solutions to account for the estimation error. Managerial implications: The closed-form solutions enable an efficient computation of optimal inventory levels. In addition, we explore the property of optimal robust inventory levels with respect to the nonrobust version via concepts of perceived critical ratio and mean repulsion. The results of numerical experiments and the case study indicate that the proposed model outperforms other state-of-the-art approaches, particularly in environments where demand is influenced by covariates and difficult to estimate. Funding: X. Li is supported by the Singapore Ministry of Education [Tier 1 Grant 23-0619-P0001, 24-0500-A0001] and National Natural Science Foundation of China [Grant 72331004]. L. Zhang is partially supported by the National Natural Science Foundation of China [Grants 72171156 and 72231002] and the Hong Kong Research Grants Council [Grant 16212419]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0159. [ABSTRACT FROM AUTHOR]

We develop and implement methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for prospect investors. We formulate a new testing procedure for prospect spanning for two nested portfolio sets based on subsampling and linear programming. In an application, we use the prospect spanning framework to evaluate whether well-known anomalies are spanned by standard factors. We find that of the strategies considered, a few of them expand the opportunity set of the prospect type investors and thus have real economic value for them and involve absence of loss aversion. Those are the net stock issue anomaly under the FF-5 model, the momentum and net stock issue anomalies under the M-4 model, and the momentum anomaly under the q model. In-sample and out-of-sample results prove remarkably consistent in identifying genuine anomalies for prospect investors. This paper was accepted by Will Cong, finance. Supplemental Material: The data and online appendix are available at https://doi.org/10.1287/mnsc.2023.4953. [ABSTRACT FROM AUTHOR]

This study aims to conduct an empirical comparative analysis of the performance of Shari’ah and conventional stock indexes during the period 2017–2023, which includes the COVID-19 pandemic. Additionally, it aims to investigate investors’ preferences and analyse the long-term relationship of these indexes, as well as exploring the potential diversification benefits. The research methodology incorporates stochastic dominance analysis, the VARMAX procedure, and Johansen’s co-integration approach. The data utilized consists of 31 conventional and 31 Islamic stock indexes, specifically from the FTSE, DJ, MSCI, and S&P series.

Introduction: This article introduces a new family of weighted mixture distributions, referred to as θ-WM. The θ-WM family is generated by combining two distributions weighted by a parameter θ, offering notable flexibility to model a wide range of complex phenomena. A special case study of the θ-weighted mixture distribution of Weibull-Lomax (θ-WMWLx) is included, resulting from the combination of Weibull and Lomax distributions. Methods: The research thoroughly examines the reliability and statistical properties of the θ-WMWLx distribution. Key aspects such as stochastic dominance, survival and hazard functions, mean residual life, and moments are addressed. The maximum likelihood method is used to estimate unknown parameters. Results: The research findings show that the θ-WMWLx distribution provides a superior fit compared to competing distributions. The analyses are validated using three real datasets, demonstrating the effectiveness of the proposed distribution. Discussion: The θ-WMWLx distribution stands out for its ability to model complex phenomena with high precision. Validation with real data confirms that the proposed distribution offers a better fit than existing distributions, highlighting its utility and applicability in various statistical analysis contexts. [ABSTRACT FROM AUTHOR]

This paper proposes a novel multi-attribute decision-making (MADM) method for interval rough numbers (IRNs) considering different distribution types, namely uniform, exponential, and normal distributions. Upper and lower approximate interval dominance degrees are defined and aggregated using dynamic weights to obtain pairwise comparisons of IRNs. The properties of dominance are verified, and an attribute weight determination method based on the dominance balance degree is introduced. The proposed MADM method is data-driven and does not rely on the subjective preferences of decision-makers. Case analysis demonstrates the effectiveness and rationality of the proposed method, revealing that the distribution type of IRNs significantly impacts decision results, potentially leading to reversed ranking outcomes. The proposed method offers a comprehensive framework for handling MADM problems with IRNs under different distributions. [ABSTRACT FROM AUTHOR]

The paper analyses optimal spending of an endowment fund. The purpose is to find a spending rule which is optimal for the owners and which secures that the fund will last "forever". This we do by finding closed form solutions of the optimal consumption to wealth ratio. We solve this problem using the life cycle model, where the agent can have preferences represented by expected utility or recursive utility. We apply our results to a sovereign wealth fund, and demonstrate that the optimal spending rate is significantly lower than the fund's expected real rate of return, a rule which is in common use. Employing the latter as the spending rate, implies that the fund's value deteriorates both in probability and in expectation, as time goes. For both kinds of long term convergence we find closed form threshold values. Spending below these values secures a sustainable fund. [ABSTRACT FROM AUTHOR]

In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. We show that, for strict preferences, the unique strong core allocation "respects improvement"—if an agent's object becomes more desirable for some other agents, then the agent's allotment in the unique strong core allocation weakly improves. We extend this result to weak preferences for both the strong core (conditional on nonemptiness) and the set of competitive allocations (using probabilistic allocations and stochastic dominance). There are no counterparts of the latter two results in the two-sided matching literature. We provide examples to show how our results break down when there is a bound on the length of exchange cycles. Respecting improvements is an important property for applications of the housing markets model, such as kidney exchange: it incentivizes each patient to bring the best possible set of donors to the market. We conduct computer simulations using markets that resemble the pools of kidney exchange programs. We compare the game-theoretical solutions with current techniques (maximum size and maximum weight allocations) in terms of violations of the respecting improvement property. We find that game-theoretical solutions fare much better at respecting improvements even when exchange cycles are bounded, and they do so at a low efficiency cost. As a stepping stone for our simulations, we provide novel integer programming formulations for computing core, competitive, and strong core allocations. Funding: P. Biró gratefully acknowledges financial support from the Hungarian Scientific Research Fund, OTKA [Grant K143858] and the Hungarian Academy of Sciences [Grant LP2021-2]. F. Klijn gratefully acknowledges financial support from AGAUR–Generalitat de Catalunya [Grants 2017-SGR-1359 and 2021-SGR-00416] and the Spanish Agencia Estatal de Investigación [Grants ECO2017-88130-P and PID2020-114251GB-I00] (funded by MCIN/AEI/10.13039/501100011033) and the Severo Ochoa Programme for Centres of Excellence in R&D (Barcelona School of Economics) [Grant CEX2019-000915-S]. Research visits related to this work were financed by COST Action [Grant CA15210 ENCKEP], supported by COST (European Cooperation in Science and Technology), http://www.cost.eu/. [ABSTRACT FROM AUTHOR]

The present research discusses the application of risk management tools and Real Option Analysis (ROA) to assess and quantify managerial flexibility in machine replacement decisions under uncertain conditions. Different management configurations are used for the real options approach: options to execute, options to delay, and options to cancel. This reflects the uncertainty inherent to each stage of planning. Uncertainties such as future demand and life-cycle costs are implemented in the model as probability distributions. Monte Carlo simulation is employed to deal with such uncertainties and to facilitate experimental trials. The net present value is used as a decision criterion to determine the best replacement option under different replacement and real option scenarios. Herein, a case study to evaluate different replacement alternatives was conducted for the garment industry. Results of the stochastic net present value, mean-standard-deviation scatter plot, and stochastic dominance showed that the best option was to rent and then buy a new machine of reduced size but greater technological advancement. Finally, tornado diagrams and perfect control methods were used to analyze uncertain factors in order to improve the model and further minimize uncertainty effects. [ABSTRACT FROM AUTHOR]

Abstract.In this note, we present an overlooked result derived from Fishburn’s Convex Stochastic Dominance (CSD) (Fishburn (1974a; 1974b). We demonstrate that CSD is a sufficient condition for establishing second-order stochastic dominance in the context of linear combinations of random variables. While this result may appear straightforward, to the best of our knowledge, it has not been explicitly presented as we have done in this work. Furthermore, the implications of this finding are extensive, as it can be applied to various areas of research, as we illustrate in this study. [ABSTRACT FROM AUTHOR]

True benevolence is, most fundamentally, a desire that the world be better. It is natural and common, however, to frame thinking about benevolence indirectly, in terms of a desire to make a difference to how good the world is. This would be an innocuous shift if desires to make a difference were extensionally equivalent to desires that the world be better. This paper shows that at least on some common ways of making a "desire to make a difference" precise, this extensional equivalence fails. Where it fails, "difference-making preferences" run counter to the ideals of benevolence. In particular, in the context of decision making under uncertainty, coupling a "difference-making" framing in a natural way with risk aversion leads to preferences that violate stochastic dominance, and that lead to a strong form of collective defeat, from the point of view of betterness. Difference-making framings and true benevolence are not strictly mutually inconsistent, but agents seeking to implement true benevolence must take care to avoid the various pitfalls that we outline. [ABSTRACT FROM AUTHOR]

We characterize conditions under which a better consumption distribution implies higher welfare. Specifically, here "better consumption" means first‐order stochastic dominance, and "higher welfare" means higher expected utility for every subpopulation of individuals with the same utility function. Although this implication seems natural, we first provide a counterexample wherein better consumption risk allocation outweighs lower consumption. We then show that higher expected utility results from higher consumption in different settings, including fixed dependence (fixed copula) between consumption and individual risk preferences, or alternatively using the rank invariance assumption from the treatment effects literature. These are discussed in several real‐world examples. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach to estimating the minimum variance hedge ratio (MVHR) based on the wild bootstrap and evaluates the approach using a spectrum of conservative to aggressive alternative hedging strategies associated with the percentiles of the MVHR's bootstrap distribution. This approach is suggested to be more informative and effective relative to the conventional method of hedging solely based on a single-point estimate. Furthermore, the percentile-based MVHRs are robust to influential outliers, non-normality, and unknown forms of heteroskedasticity. The bootstrap percentile-based hedging strategies' effectiveness is compared with those from the naïve method and the asymmetric DCC-GARCH model for a range of financial assets and commodities. The bootstrap percentile-based hedging technique is identified to outperform its alternatives in terms of hedging effectiveness, downside risk, and return variability, suggesting its superiority to other methods in both the literature and in practice. [ABSTRACT FROM AUTHOR]

The investment horizon plays a crucial role in portfolio selection: For horizons approximately up to a year, one can safely employ the mean–variance (M-V) rule. Moreover, if investment consultants use monthly rates of return to derive the M-V efficient set and the investor horizon is longer but smaller than one year, the economic cost induced by this horizon mismatch is negligible. For longer horizons, the M-V rule deviates substantially from expected utility maximization and the economic cost induced by employing the M-V rule is substantial. For relatively long horizons (say 20 or 30 years), despite the argument that with myopic preference the horizon does not matter, small stocks dominate large stocks by the maximum geometric mean (MGM) rule and, in practice, also by expected utility for all economically relevant preferences, as there is almost first-degree stochastic dominance (AFSD). [ABSTRACT FROM AUTHOR]

Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two distributions, I propose statistical inference methods to learn about the set of utility functions for which the first distribution has higher expected utility than the second distribution. With high probability, an "inner" confidence set is contained within this true set, while an "outer" confidence set contains the true set. Such confidence sets can be formed by inverting a proposed multiple testing procedure that controls the familywise error rate. Theoretical justification comes from empirical process results, given that very large classes of utility functions are generally Donsker (subject to finite moments). The theory additionally justifies a uniform (over utility functions) confidence band of expected utility differences, as well as tests with a utility-based "restricted stochastic dominance" as either the null or alternative hypothesis. Simulated and empirical examples illustrate the methodology. [ABSTRACT FROM AUTHOR]

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision‐making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of non‐expected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes. [ABSTRACT FROM AUTHOR]

The Entscheidungsnavi is an open-source decision support system based on multi-attribute utility theory, that offers various methods for dealing with uncertainties. To model decisions with uncertainties, decision-makers can use two categories: Forecast and Parameter Uncertainties. Forecast Uncertainty is modeled with (combined) influence factors using discrete, user-defined probability distributions or predefined 'worst-median-best' distributions. Parameter Uncertainty allows imprecision for utilities, objective weights, and probability distributions. To analyze these uncertainties, the Entscheidungsnavi offers several methods and tools, like a robustness check, based on (Monte Carlo) simulations and a sensitivity analysis. The objective weight analysis provides insights into the effects of different objective weight combinations. Indicator impacts, tornado diagrams, and risk profiles visualize the impact of uncertainties in a decision under risk. Risk profiles also enable a check for stochastic and simulation dominance. This article presents the complete range of methods for dealing with uncertainties in the Entscheidungsnavi using a hypothetical case study. [ABSTRACT FROM AUTHOR]

Cryptocurrency returns are highly nonnormal, casting doubt on the standard performance metrics. We apply almost stochastic dominance, which does not require any assumption about the return distribution or degree of risk aversion. From 29 long–short cryptocurrency factor portfolios, we find eight that dominate our four benchmarks. Their returns cannot be fully explained by the three‐factor coin model of Liu et al. So we develop a new three‐factor model where momentum is replaced by a mispricing factor based on size and risk‐adjusted momentum, which significantly improves pricing performance. [ABSTRACT FROM AUTHOR]

Summary: Location choices of differently skilled workers are analyzed in previous work on labor mobility, which proposes a model that suggests thicker tails in the skill distributions of large cities. This paper replicates the empirical findings of this work by using quantile regression and density plots as employed in the existing study, while also suggesting an alternative testing method for thick tails in the form of an initial stochastic dominance test. The test reveals clear evidence of a thicker lower tail, but the results are less clear for the upper tail, which raises some questions on how to best handle extreme upper tails of skill distributions. [ABSTRACT FROM AUTHOR]

I examine the design of optimal insurance contracts considering the possibility of government disaster relief payments. This work focuses on the impact of (risky and ambiguous) government disaster relief on the shape of optimal private insurance contracts. I demonstrate that the optimal insurance contract is a straight deductible contract in the case of a fixed probability of government relief. This result is robust to ambiguity in the probability of relief payments, even for ambiguity‐averse decision makers. If government disaster relief becomes more likely for larger losses, then the optimal insurance contract features coinsurance above a deductible. I also extend this analysis to more general stochastic dominance relationships between disaster relief and loss magnitude. [ABSTRACT FROM AUTHOR]

This paper presents the first comprehensive study of a data-driven formulation of the distributionally robust second order stochastic dominance constrained problem (DRSSDCP) that hinges on using a type-1 Wasserstein ambiguity set. It is, furthermore, for the first time shown to be axiomatically motivated in an environment with distribution ambiguity. We formulate the DRSSDCP as a multistage robust optimization problem and further propose a tractable conservative approximation that exploits finite adaptability and a scenario-based lower bounding problem. We then propose the first exact optimization algorithm for this DRSSDCP. We illustrate how the data-driven DRSSDCP can be applied in practice on resource-allocation problems with both synthetic and real data. Our empirical results show that, with a proper adjustment of the size of the Wasserstein ball, DRSSDCP can reach acceptable out-of-sample feasibility yet still generating strictly better performance than what is achieved by the reference strategy. Optimization with stochastic dominance constraints has recently received an increasing amount of attention in the quantitative risk management literature. Instead of requiring that the probabilistic description of the uncertain parameters be exactly known, this paper presents a comprehensive study of a data-driven formulation of the distributionally robust second order stochastic dominance constrained problem (DRSSDCP) that hinges on using a type-1 Wasserstein ambiguity set. This formulation allows us to identify solutions with finite sample guarantees and solutions that are asymptotically consistent when observations are independent and identically distributed. It is, furthermore, shown to be axiomatically motivated in an environment with distribution ambiguity. Leveraging recent results in the field of robust optimization, we further formulate the DRSSDCP as a multistage robust optimization problem and further propose a tractable conservative approximation that exploits finite adaptability and a scenario-based lower bounding problem, both of which can reduce to linear programs under mild conditions. We then propose, to the best of our knowledge, the first exact optimization algorithm for this DRSSDCP, the efficiency of which is confirmed by our numerical results. Finally, we illustrate how the data-driven DRSSDCP can be applied in practice on resource-allocation problems with both synthetic and real data. Our empirical results show that, with a proper adjustment of the size of the Wasserstein ball, DRSSDCP can reach "acceptable" out-of-sample feasibility yet still generating strictly better performance than what is achieved by the reference strategy. Funding: This research was partially supported by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2016-05208], the Canada Research Chair program [Grant 950-230057], and Groupe d'études et de recherche en analyse des décisions, and it was enabled in part by support provided by Calcul Quebec (https://www.calculquebec.ca/en/) and the Digital Research Alliance of Canada (https://www.alliancecan.ca/). Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2387. [ABSTRACT FROM AUTHOR]

We study statistical properties of the optimal value of the sample average approximation (SAA). The focus is on the tail function of the absolute error induced by the SAA, deriving upper estimates of its outcomes dependent on the sample size. The estimates allow to conclude immediately convergence rates for the optimal value of the SAA. As a crucial point, the investigations are based on new types of conditions from the theory of empirical processes which do not rely on pathwise analytical properties of the goal functions. In particular, continuity in the parameter is not imposed in advance as often in the literature on the SAA method. It is also shown that the new condition is satisfied if the paths of the goal functions are H\"older continuous so that the main results carry over in this case. Moreover, the main results are applied to goal functions whose paths are piecewise H\"older continuous as, e.g., in two-stage mixed-integer programs. The main results are shown for classical risk-neutral stochastic programs, but we also demonstrate how to apply them to the sample average approximation of risk-averse stochastic programs. In this respect, we consider stochastic programs expressed in terms of mean upper semideviations and divergence risk measures. [ABSTRACT FROM AUTHOR]

This paper examines the Efficient Market Hypothesis (EMH) in crude oil amid the "financialization of commodity markets" and the "fracking revolution". It applies the generalized spectral derivative test (Hong and Lee 2005) on both West Texas Intermediate and Brent spot and futures markets, alongside a stochastic dominance test (Linton et al., 2005) to investigate arbitrage opportunities across markets and benchmarks. The findings indicate that financialization has made each market more efficient but also created more arbitrage opportunities in spot‐futures markets at both benchmarks. The fracking revolution has fragmented oil markets but had little impact on EMH in individual markets or across markets. [ABSTRACT FROM AUTHOR]

We contribute to redefining the criteria based on Almost Stochastic Dominance for better portfolio comparison in four ways. First, we refine the first order of Marginal Conditional Stochastic Dominance (Yitzhaki and Olkin in Concentration indices and concentration curves, Vol 19, Lecture notes-monograph series: stochastic orders and decision under risk, 1991; Shalit and Yitzhaki in Manag Sci 40(5):670–684, 1994), which is designed for pairwise asset comparison. Second, we redefine Almost Marginal Conditional Stochastic Dominance (AMCSD) by Denuit et al. (J Bank Finance 41:57–66, 2014) and Chen et al. (Q Rev Econ Finance 85 (C):260–269, 2022), which considers multiple asset changes in a portfolio, especially in the case of second-order stochastic dominance. Our effort secures the hierarchy property (Guo et al. in Econ Lett 121:252–256, 2013) which is absent in previous studies. Third, we extend the analysis of multiple assets and apply our AMCSD definition and Marginal Conditional Stochastic Dominance. Our AMCSD treatment is confirmed to be more appropriate than those in previous study. Finally, for the sake of portfolio risk management, we compose three hypothetical portfolios with option-based indices for empirical analysis. The empirical outcomes support our efforts. [ABSTRACT FROM AUTHOR]

Consider a renewal risk model with stochastic return and stochastic perturbation, where the price process of the investment portfolio is a geometric Lévy process. When the claim sizes have a dependence structure, we derive the asymptotics of the finite-time ruin probability for all subexponential claim sizes. Particularly, when the claim sizes come from a subclass of the subexponential distribution class, the finite-time ruin probability has been estimated for claim sizes with a general dependence structure. [ABSTRACT FROM AUTHOR]

Discontinuities largely influence the mechanical properties of rock joints. However, discontinuity orientation clustering methods often rely on the aggregation and separation of orientation data without full consideration of the prior probability structure of orientation data. This paper proposes a method of optimal clustering by Fisher mixed distribution (OCFMD) for automatic grouping of discontinuity orientation. Based on the Fisher prior probability structure of orientation data, OCFMD can identify optimal group centers and group numbers by balancing the fitting accuracy and dominance of Fisher mixed distributions, and optimal grouping results can be generated by membership calculation. A Newton–Raphson expectation maximization (NR-EM) algorithm is derived for the parameter fitting of Fisher mixed distributions. The Fibonacci sequence is used to generate sample points. In addition, the neighbor probability and density of sample points based on Fisher mixed distributions is derived for fitting accuracy calculation. Several cases of rock slopes and rock tunnel excavation faces are adopted for analyzation. Three clustering algorithms combined with four clustering validity indexes of discontinuity grouping are used for comparison. The results show that OCFMD is more accurate and robust than the other automatic grouping methods in optimal grouping result generation. Highlights: An automatic optimal clustering method of discontinuity orientation is proposed based on Fisher mixed distributions. The balance between fitting accuracy and dominance of Fisher mixed distributions is derived for the selection of optimal grouping results. The grouping results of several traditional clustering algorithms combined with clustering validity indexes are observed to be inconsistent with manual results. The proposed method is more accurate and robust than the compared traditional methods in optimal grouping result generation. The convergence effectiveness, sensitivity of neighbor angle selection and robustness to normal vector variations are validated. [ABSTRACT FROM AUTHOR]

Efficiency plays a crucial role in portfolio optimization. This notion is formulated by means of stochastic optimization techniques. Very often this problem is subject to partial uncertainty or incomplete information on the probability distribution and on the preferences expressed by means of the utility function. In this case both the objective function and the underlying probability measure are not known with precision. To address this kind of issues, we propose to model the notion of incomplete information by means of set-valued analysis and, therefore, we propose two different extensions of the classical model. In the first one we rely on the notion of set-valued function while the second one utilizes the notion of set-valued probability. For both of them we investigate stability properties. These results are also linked to the notion of robustness of the aforementioned problem. Finally we apply the obtained results to portfolio theory and stochastic dominance. [ABSTRACT FROM AUTHOR]

This paper investigates the coherence of a new class of ratio-based inequality indices introduced in Chan (2022) with respect to certain partial orderings of the underlying income distributions. While coherence with respect to stochastic dominance has been extensively studied, the appropriate partial ordering for this new class of indices is quantile ratio dominance. This paper also establishes coherence with respect to quantile ratio dominance for some other classes of inequality indices which have been introduced by other authors. Finally, some connections between the notion of coherence and transfer principles are explored. [ABSTRACT FROM AUTHOR]

• Information-theoretic approach tracks wage gap while capturing inequality in distributions. • Applying this approach to South African data shows that convergence of the gender gap is faster under the entropy measure. • Men's wages stochastically dominate women's wages only for evaluation functions that are sensitive to inequality. • The difference between the male and female wage distributions is largely driven by the wage structure effect. • We argue for the use of inequality sensitive measure when tracking gender wage gap. We examine the trend in the gender wage gap in South Africa taking into consideration the high level of general inequality in the country. To do this, we utilize the information-theoretic approach of the Generalised Entropy (GE) measures of divergence supplemented by stochastic dominance analysis and tests. Under this approach, male and female wage distributions are summarized by suitable evaluation functions and then the difference between the evaluations is computed. Unlike conventional measures of the gender wage gap based on the mean and quantiles, this approach does not assume rank invariance and makes explicit the evaluation functions used. We find that the rate of convergence of the gender wage gap depends on the measure used to aggregate the gap across the entire distribution. Comparison of the aggregate measures of the gender wage gap (mean, median and the entropy measure) reveals that the convergence of the gender wage gap is faster under the entropy measure. This is because unlike the mean, the entropy measure captures the dispersion of wages across individuals. Stochastic dominance test results reveal that male wages dominate female wages mostly in the second-order sense i.e., only for evaluation functions that are increasing in wages and concave. Finally, decomposition results show that across measures, the persistent gender wage gap is attributable to wage structure effects as opposed to composition effects. Therefore, to effectively address the persistent gender wage gap in the middle of the income distribution, policies should be geared towards the returns to characteristics at the median. The implication of these findings is that measures of the gender wage gap that ignore the overall inequality are likely to skew the estimate of the gender wage gap. [ABSTRACT FROM AUTHOR]

The US Space Force's competitive endurance framework may exacerbate offense-defense balance problems in space. Applying concepts of realism, the security dilemma, and offense-defense balance to the notion of competitive endurance supports a new theory of offense dominance in the space domain. Specifically, advances in military technology, space mobility and logistics, and space domain awareness provide an advantage to attackers and increase the probability of conflict in space. By prioritizing defense-focused technology development, defense-centric doctrine and tactics, and greater information-sharing, the Space Force can offset the factors driving increased advantage to the offense and decrease the likelihood of conflict. [ABSTRACT FROM AUTHOR]

Expected returns, variances, betas, and alphas are all non-linear functions of the investment horizon. This seems to be a fatal conceptual problem for the capital asset pricing model (CAPM), which assumes a unique common horizon for all investors. We show that under the standard assumptions, the theoretical CAPM equilibrium surprisingly holds with the 1-period parameters, even when investors have heterogeneous and possibly much longer horizons. This is true not only for risk-averse investors, but for any investors with non-decreasing preferences, including prospect theory investors. Thus, the widespread practice of using monthly betas to estimate the cost of capital is theoretically justified. [ABSTRACT FROM AUTHOR]

The decision of farmers to reduce fertilizer applications and, thus, the achievement of agri‐environmental policy goals interacts with market price developments. In this study, we analyze how changes in price levels and volatility over time (i.e., 1991–2006 vs. 2007–2022) affected farmers' preferences to reduce fertilizer application using statistical inferences of stochastic dominances. The analysis considers two cropping systems and fertilizer reduction measures: (i) grassland‐based milk production and the use of legumes and (ii) wheat production and the use of variable rate application. We show that the economic value of reducing fertilizer increased over time in both grassland‐based milk and wheat production. However, only in the case of wheat production was the reduction in fertilizer application observed as more risk‐reducing over time. In contrast, in grassland‐based milk production, the co‐movement of fertilizer and milk prices canceled out the increase in risk reduction. We conclude that changes in market price, along with agri‐environmental subsidies, can increasingly incentivize the reduction of fertilizer use. [ABSTRACT FROM AUTHOR]

For most major movies, consumers have a choice to watch them in a theater or on home video. While each viewing channel has its own advantages and disadvantages, consumers are watching the same underlying product—a specific movie. An unanswered question is whether consumers enjoy watching a specific movie more in a theater or video setting. Using IMDb rating data, we find that for most wide-release movies, ratings are higher during the theater window than during the video window. The differences are particularly high for movies with relatively large production budgets and for sequels. [ABSTRACT FROM AUTHOR]

This paper considers a moral hazard problem where the agent can choose any output distribution with a support in a given compact set. The agent's effort‐cost is smooth and increasing in first‐order stochastic dominance. To analyze this model, we develop a generalized notion of the first‐order approach applicable to optimization problems over measures. We demonstrate each output distribution can be implemented and identify those contracts that implement that distribution. These contracts are characterized by a simple first‐order condition for each output that equates the agent's marginal cost of changing the implemented distribution around that output with its marginal benefit. Furthermore, the agent's wage is shown to be increasing in output. Finally, we consider the problem of a profit‐maximizing principal and provide a first‐order characterization of principal‐optimal distributions. [ABSTRACT FROM AUTHOR]

Recent theoretical and empirical advancements highlight the pivotal role played by higher-order moments, such as skewness, in shaping financial decision-making. Nevertheless, contemporary experimental research predominantly relies on limited-outcome lotteries, an oversimplified representation distant from real-world investment dynamics. To bridge this research gap, we conducted a rigorously pre-registered experiment. Our study delves into individuals' preferences for investment opportunities, examining the influence of skewness of continuous probability distributions of returns. We document an inclination towards positively skewed outcome distributions. Furthermore, we uncovered a substitution effect between risk appetite and the sign of skewness. Finally, we unveiled a robust positive correlation between skewness-seeking behavior and a propensity for speculative behavior. Simultaneously, a distinct negative correlation surfaced between skewness-seeking behavior and the perceived risk associated with positive skewness. [ABSTRACT FROM AUTHOR]

Sequencing decisions in mixed-model assembly lines are complicated by various uncertainty factors. This paper addresses a real-life uncertainty factor identified in a manufacturer of large vehicles, by modelling unreliable part delivery and quality. Stochastic optimisation is applied to find sequencing policies that improve the on-time performance of its mixed-model assembly lines. As schedulers have different levels of risk aversion, a risk-averse programme is further presented to protect against the decision maker's chosen fraction of worst scenarios. Computational studies with Progressive Hedging as the solution method, and its lower bounding approach, demonstrate the high quality of resulting sequencing decisions and the time efficiency of the solution method. [ABSTRACT FROM AUTHOR]

To test the relationships of stochastic dominance, this paper firstly proposes two new consistent K-S-type statistics based on a quantile rule. Then, we consider their asymptotic properties. We introduce the bootstrap method to calculate the p-values of our proposed tests and use the Monte Carlo method to compare the power of our proposed test with the DD test and the BD test. The simulations showed that our test performed better than these two tests. Finally, we applied our proposed tests to compare the visibility of four provinces in China and compared the effects with the DD test and BD test. The empirical results showed that the conclusions of our proposed method are more-consistent with the dominance relationships of the four provinces. For a given significance level, the results of our proposed test demonstrate that the visibility of Jiangxi province is the best. The next one is the visibility of Hubei province, which outperforms the visibility of Anhui province. The visibility of Hunan province is the poorest. [ABSTRACT FROM AUTHOR]

This study considers the problem of random assignment of a set of objects to a set of agents based on strict ordinal preferences of the agents. We analyze the fractional Boston rule, which is a generalization of the classical Boston rule to random assignment environments. We introduce two new axioms—stochastic dominance (sd)-rank-efficiency and equal-rank envy-freeness—which are respectively efficiency and fairness conditions that respect preference ranks. Sd-rank-efficiency implies ordinal efficiency, which is an efficiency concept defined by Bogomolnaia and Moulin (J Econ Theory 100(2):295–328, 2001) for random assignment environments in the sense of first-order stochastic dominance. Equal-rank envy-freeness implies equal treatment of equals. Sd-rank-efficiency and equal-rank envy-freeness characterize the fractional Boston rule. [ABSTRACT FROM AUTHOR]