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Existing accounts of social insurance tend to treat social risks as given and ask whether it is justified for the state to deal with these risks for its citizens. They ignore that many common risks are in fact imposed on citizens as a byproduct of the institutional choices of the society, which call for justification in the first place. In this paper, I use the Scanlonian contractualist framework to develop an account of just social risk imposition which implies a demand for fair risk sharing by all members of a society. In particular, I defend a compensation principle which requires that compensation be paid to victims of risk materialisation. This duty of paying should be shared by all those who benefit from the imposition of the relevant risk. I suggest that this provides a case for social insurance as a way of fairly sharing the burden of social risks.

Catastrophe insurance markets fail to provide sufficient protections against natural catastrophes, whereas they have the capacity to absorb the losses. In this paper, we assume the catastrophic risks are dependent and extremely heavy-tailed, and insurers have limited liability to cover losses up to a certain amount. We provide a comprehensive study to show that the diversification in the catastrophe insurance markets can be transited from suboptimal to preferred by increasing the number of insurers in the market. This highlights the importance of coordination among insurers and the government intervention in encouraging insurers to participate in the catastrophe insurance market to exploit risk sharing. Simulation studies are provided to illuminate the key findings of our results.

Denuit (2019, 2020a) demonstrated that conditional mean risk sharing introduced by Denuit and Dhaene (2012) is the appropriate theoretical tool to share losses in collaborative peer-to-peer insurance schemes. Denuit and Robert (2020a, 2020b, 2021) studied this risk sharing mechanism and established several attractive properties including linear approximations when total losses or the number of participants get large. It is also shown there that the conditional expectation defining the conditional mean risk sharing is asymptotically increasing in the total loss (under mild technical assumptions). This ensures that the risk exchange is Pareto-optimal and that all participants have an interest to keep total losses as small as possible. In this article, we design a flexible system where entry prices can be made attractive compared to the premium of a regular, commercial insurance contract and participants are awarded cash-backs in case of favorable experience while being protected by a stop-loss treaty in the opposite case. Members can also be grouped according to some meaningful criteria, resulting in a hierarchical decomposition of the community. The particular case where realized losses are allocated in proportion to the pure premiums is studied.

Due to the risks involved in not achieving desired health outcomes for the dollar spent on drugs, healthcare decision makers, including payers, providers, drug manufacturers, and patients, need a mechanism to share this financial risk among the involved parties. Performance-based risk-sharing arrangements (PBRSAs) are agreements that can potentially reduce the 'drug lag' in which patients wait for an unknown amount of time until a particular drug is covered under their health plan. In addition, PBRSAs can mitigate the risk of investing heavily in drugs that are ineffective or do not deliver good value or "bang for the buck". This review describes and evaluates PBRSAs for drugs in the USA and juxtaposes to other developed nations (i.e. Germany) that adopted PBRSAs in their healthcare model. There are different types of outcomes-based health schemes, namely conditional coverage, which can be further broken down into coverage with evidence development (CED), conditional treatment continuation (CTC), and performance-linked reimbursement, which includes outcomes guarantees. Both CED and CTC are 'conditional' on the collected evidence of the new drug's effectiveness, offering discount only if the drug delivers desirable results. The outcomes guarantee scheme offers discount or even a full refund if the outcome is less than expected, forcing the drug to meet the expected effectiveness. The USA can follow the German reference pricing model in which the assessment of new drugs is centralized and done collectively by representatives from a group of healthcare decision makers. In any shape or form, PBRSA is a clever mechanism to cope with uncertainty if drug price is scaled appropriately based on value.

Motivated by macroeconomic risks, such as the COVID-19 pandemic, we consider different risk management setups and study efficient insurance schemes in the presence of low probability shock events that trigger losses for all participants. More precisely, we consider three platforms: the risk-sharing, insurance and market platform. First, we show that under a non-discriminatory insurance assumption, it is optimal for everybody to equally share all risk in the market. This gives rise to a new concept of a contingent premium which collects the premia ex-post after the losses are realised. Insurance is then a mechanism to redistribute wealth, and we call this a risk-sharing solution. Second, we show that in an insurance platform, where the insurance is regulated, the tail events are not shared, but borne by the government. Third, in a competitive market we see how a classical solution can raise the risk of insolvency. Moreover, in a decentralised market, the equilibrium cannot be reached if there is adequate sensitivity to the common shock events. In addition, we have applied our theory to a case where the losses are calibrated based on the UK Coronavirus Job Retention Scheme.

In this paper, we address the optimal funding of pensions by means of portfolio choice approach. Considering the unfunded (Paygo) pension system as a ‘quasi-asset’ with hedging and diversif...

We introduce bilateral risk aversion into the mixed adverse selection - moral hazard model of Laffont and Tirole (1986). The presence of exogenous risk interacts with the adverse selection problem in interesting ways. In particular, we show that it is never optimal to present the firm with a fixed price contract, that the efficient firm typically bears more risk than the inefficient firm, and that an increase in exogenous risk may bring about a decrease in expected cost of the project. As a by-product, we also establish that the famous ‘no-distortion-on-the top’ result in adverse selection models relies on risk neutrality of the agent.

This paper studies the optimal risk-sharing between an insurer and a reinsurer. The insurer purchases reinsurance for risk-control and decides her retention level with an objective to minimize her ruin probability. The reinsurer has control over the reinsurance price and aims to maximize her expected discounted profits up to the time when the insurer goes bankrupt. In a stochastic differential game-theoretic framework, we determine the insurer’s optimal reinsurance strategy and specify the reinsurance contract by solving a system of coupled Hamilton–Jacobi–Bellman equations. We obtain explicit solutions for the game problem when both the insurance and the reinsurance premiums are calculated according to the standard-deviation principle or the expected value principle, respectively. Our results show that, depending on the model parameters, the reinsurance contract is either provided with a peak price when the insurer has sufficient cash reserve and with a minimum price when otherwise, or is always provided with a peak price. We also perform some numerical analyses and provide economic interpretations for the results.

In this paper, we propose two financial-longevity risk-sharing methods based on an existing risk-linked annuity. Within a specific framework, we first propose the risk-sharing group self-annuitization (GSA), where different proportions of financial and longevity risks are shared between a group of annuitants and the insurer. Secondly, we propose the complete risk-sharing GSA. We implicitly define a set of annuity products which depend on the risk proportion borne by a group of annuitants. The defined set of annuities goes from the classical annuity to the GSA.

Background. Pharmaceutical risk sharing agreements (RSAs) are commonly used to manage uncertainties in costs and/or clinical benefits when new drugs are added to a formulary. However, existing mathematical models of RSAs ignore the impact of RSAs on clinical and financial risk. Methods. We develop a model in which the number of patients, total drug consumption per patient, and incremental health benefits per patient are uncertain at the time of the introduction of a new drug. We use the model to evaluate the impact of six common RSAs on total drug costs and total net monetary benefit (NMB). Results. We show that, relative to not having an RSA in place, each RSA reduces expected total drug costs and increases expected total NMB. Each RSA also improves two measures of risk by reducing the probability that total drug costs exceed any threshold and reducing the probability of obtaining negative NMB. However, the effects on variance in both NMB and total drug costs are mixed. In some cases, relative to not having an RSA in place, implementing an RSA can increase variability in total drug costs or total NMB. We also show that, for some RSAs, when their parameters are adjusted so that they have the same impact on expected total drug cost, they can be rank-ordered in terms of their impact on variance in drug costs. Conclusions. Although all RSAs reduce expected total drug costs and increase expected total NMB, some RSAs may actually have the undesirable effect of increasing risk. Payers and formulary managers should be aware of these mean-variance tradeoffs and the potentially unintended results of RSAs when designing and negotiating RSAs.

The price of new brand-name prescription drugs has been rising fast in the United States. For example, the Amgen cholesterol drug Repatha had an initial list price of $14,523 per year. Patients, even with insurance coverage, must pay out of pocket a significant portion of this price. The treatment might not be successful, and this possibility reduces risk-sensitive patients’ incentives to purchase the drug. The high price together with the chance of negative treatment outcomes may lead payers to deny coverage for the drug. Outcome-based pricing has been proposed as a way to reallocate the risks and improve both payer resource allocation and patient access to drugs. According to an outcome-based rebate contract between Amgen and Harvard Pilgrim Healthcare, if a patient on Repatha suffers a heart attack or a stroke, both patient and insurer are refunded the cost of the drug. We use a stylized model to analyze the effect of outcome-based pricing via rebates. Our model captures the interaction between heterogenous, price-sensitive, risk-sensitive patients who decide whether to purchase the drug; a payer deciding whether to provide coverage for the drug; and a price-setting pharmaceutical firm seeking to maximize expected profits. We find that, in many cases, a pharmaceutical firm and payer cannot simultaneously benefit from outcome-based pricing, and who will benefit is determined by the probability of treatment success. Outcome-based pricing thus appears unlikely to solve the issues of high drug prices and high payer expenditures. However, supplementing outcome-based pricing with a transfer payment from firm to payer can make payer and firm (but not necessarily the patients) better off than under uniform pricing when the drug has a low chance of success. This paper was accepted by Stefan Scholtes, healthcare management.

Pension reform is a crucial societal problem in many countries, and traditional pension schemes, such as Pay-As-You-Go and Defined-Benefit schemes, are being replaced by more sustainable ones. One challenge for a public pension system is the management of a systematic risk that affects all individuals in one generation (e.g., that caused by a worse economic situation). Such a risk cannot be diversified within one generation, but may be reduced by sharing with other (younger and/or older) generations, i.e., by intergenerational risk sharing (IRS). In this work, we investigate IRS in a Collective Defined-Contribution (CDC) pension system. We consider a CDC pension model with overlapping multiple generations, in which a funding-ratio-linked declaration rate is used as a means of IRS. We perform an extensive simulation study to investigate the mechanism of IRS. One of our main findings is that the IRS works particularly effectively for protecting pension participants in the worst scenarios of a tough financial market. Apart from these economic contributions, we make a simulation-methodological contribution for pension studies by employing Bayesian optimization, a modern machine learning approach to black-box optimization, in systematically searching for optimal parameters in our pension model.

Optimal risk sharing arrangements have been substantially studied in the literature, from the aspects of generalizing objective functions, incorporating more business constraints, and investigating different optimality criteria. This paper proposes an insurance model with multiple risk environments. We study the case where the two agents are endowed with the Value-at-Risk or the Tail Value-at-Risk, or when both agents are risk-neutral but have heterogeneous beliefs regarding the underlying probability distribution. We show that layer-type indemnities, within each risk environment, are Pareto optimal, which may be environment-specific. From Pareto optimality, we get that the premium can be chosen in a given interval, and we propose to allocate the gains from risk sharing equally between the buyer and seller.

In a pharmaceutical market environment with an increasing focus on “value” and long-term impact on patient outcomes, there is a natural opportunity to tie payment to performance through value-based agreements (VBAs). Seven types of VBAs are described and illustrated with case studies: pay-for-response, patient warranty, risk sharing, treatment cost capitation, budget capitation, Netflix model and mortgage model. Particularly in Europe and Australia, many deals have been made under the terms risk sharing, outcomes-based contracting, innovative contracting, patient access scheme, coverage with evidence development and managed entry agreement. Managed Entry Agreements often refer to deals made with payers as a way to address affordability and willingness-to-pay of lower- and middle-income countries in comparison with the US and Europe. An increased emphasis on providing “value,” demonstrating meaningful long-term patient outcomes and the emergence of value-based payment arrangements provide new opportunities for value-based agreements, which are often interchangeably referred to as risk sharing or innovative contracting.

Lifetime occupational exposure accounts for 42% of differences in disability risk across individuals. Incorporating this feature into a general equilibrium model, we study how social disability insurance (SDI) affects welfare through (i) the classic channel of risk-sharing and (ii) a new channel of occupational reallocation. Both channels can increase welfare, but at the optimal SDI they are at odds. Welfare gains from additional risk-sharing are reduced by overly incentivizing workers to choose risky occupations. In a calibrated economy resembling the United States, SDI increases welfare by 2.6% (consumption) relative to actuarially fair insurance. The current US system captures 92% of these gains.

In this study we model the endogenous relationship formation between risk-averse principals and agents in a CARA-normal framework. Agents exert unobservable efforts to increase mean outputs and reduce risks. We show that risk-reduction efforts are more important than mean-increasing efforts in determining the matching patterns. Compared to cases without moral hazard, the agency problem in risk reduction induces more positive-assortative matchings.

Value for money is a growing necessity in today's U.S. health care system in which drug spending is expected to increase by an average rate of 6.7% yearly through 2025. In response to uncertainty about real-world clinical and economic outcomes for many drugs, health insurers and pharmacy benefit managers (PBMs) have implemented various contracts and arrangements with drug manufacturers that can collectively be described as performance-based risk-sharing arrangements (PBRSAs). Little is known about U.S.-specific PBRSAs for drugs.To conduct a systematic review of U.S.-specific PBRSAs for drugs to describe (a) trends over time and (b) key aspects including outcome measures and terms of arrangements between stakeholders.A systematic review was conducted in MEDLINE (January 1, 1946-April 1, 2017), Embase (January 1, 1988-April 1, 2017), and the grey literature (up to April 1, 2017) to identify publicly disclosed PBRSAs. Articles and conference abstracts were included if they were published in English and described a U.S.-specific PBRSA for a drug. Articles and conference abstracts were excluded if they only described a PBRSA similar to a money-back guarantee to patients. They were also excluded if they only described a PBRSA between a PBM and a health insurer in which the latter would receive a discount for patients nonadherent to a drug. Results were summarized as counts and percentages.From the literature review, 26 publicly disclosed PBRSAs were identified. Of these, 16 (62%) were announced or initiated from 2015 to 2017, and 10 (38%) were announced or initiated from 1997 to 2012. Thirteen (50%) PBRSAs involved cardiometabolic indications; 5 (19%) involved oncology indications; and 8 (31%) involved other indications. Categorized by health insurer or PBM, 10 (38%) PBRSAs involved large multistate insurers; 5 (19%) involved the Centers for MedicareMedicaid Services; 7 (27%) involved regional insurers; 3 (12%) involved PBMs; and 1 (4%) involved multiple unspecified insurers. Regarding the most active drug manufacturers, Amgen initiated 5 (19%) PBRSAs and Novartis initiated 4 (15%). Relative to the initial FDA approval of a treatment, 15 (58%) PBRSAs were announced or initiated within 5 years, and 11 (42%) were announced or initiated more than 5 years later. For data collection, electronic medical record (EMR) data would have been an appropriate source for 12 (46%) PBRSAs; claims data would have been an appropriate source for 11 (42%) PBRSAs; and EMR and claims data would have been appropriate sources for 2 (8%) PBRSAs; no description of the outcome measures was available for 1 (4%) PBRSA.The number of publicly disclosed U.S.-specific PBRSAs for drugs has increased over the years. This review's findings confirm the interest of stakeholders in such arrangements and their confidence in the use of the selected outcome measures. Each PBRSA represents a timely collaboration among stakeholders to provide access to a drug while generating evidence to better elucidate its clinical and economic value.No funding supported this systematic review. Yu is an employee and shareholder of Allergan. Chin reports personal fees from Formulary Resources. Oh and Farias have nothing to disclose. Study concept and design were primarily contributed by Yu, along with the other authors. All authors contributed to the collection and interpretation of the data. The manuscript was written by Yu, Chin, Oh, and Farias and revised by Yu and Chin, along with the other authors.

To improve the design of the pay-out phase of DC plans, this paper proposes a new approach to structure pension products: the Personal Pension with Risk sharing (PPR). By unbundling and valuing the investment, (dis)saving, insurance and risk-sharing functions of pensions, PPRs allow risk management and (dis)saving to be customized to the specific features of heterogeneous individuals. Unlike variable annuities, PPRs allow investment risks to be combined with longevity insurance without giving rise to high year-on-year volatility in consumption streams or opaque and rigid valuation and smoothing rules. The synthesis of a PPR structure provides new opportunities for product innovation and for the comparison of retirement products.

In this work, we study the optimal risk sharing problem for an insurer between himself and a reinsurer in a dynamical insurance model known as the Kramer–Lundberg risk process, which, unlike known models, models not per claim reinsurance but rather periodic reinsurance of damages over a given time interval. Here we take into account a natural upper bound on the risk taken by the reinsurer. We solve optimal control problems on an infinite time interval for mean-variance optimality criteria: a linear utility functional and a stationary variation coefficient. We show that optimal reinsurance belongs to the class of total risk reinsurances. We establish that the most profitable reinsurance is the stop-loss reinsurance with an upper limit. We find equations for the values of parameters in optimal reinsurance strategies.

We examine the optimal size of risk pools with moral hazard. In risk pools, the effective share of the own loss borne is the sum of the direct share (the retention rate) and the indirect share borne as residual claimant. In a model with identical individuals with mixed risk-averse utility functions, we show that the effective share required to implement a specific effort increases in the pool size. This is a downside of larger pools as it, ceteris paribus, reduces risk sharing. However, we find that the benefit from diversifying the risk in larger pools always outweighs the downside of a higher effective share. We conclude that, absent transaction costs, the optimal pool size converges to infinity. In our basic model, we restrict attention to binary effort levels, but we show that our results extend to a model with continuous effort choice.

The allocation of risk among the cooperating parties in a shared project is an important decision. This is especially true in the case of large infrastructure investments. Existing risk allocation methods are either simplistic or do not consider the effect of the agents' pre-existing businesses. In this paper, we model and analyse the effect of risk sharing when two agents want to co-develop an energy infrastructure project in an uncertain environment. The cooperating agents have a pre-existing risky business, and the new common project has a deterministic initial cost but random revenue potential. Our analysis shows that the optimal risk-sharing rule depends not only on the agents' risk aversions but also on the volatility of the common project profit, the volatilities of the agents' pre-existing businesses and the correlation of each agent's pre-existing business with the common project. An illustrative example based on energy infrastructure is used to show the implications of the sharing rule for partners.

International audience; We study the dynamics of risk-sharing cooperatives among heterogeneous agents. Based of their knowledge on their risk exposure and the performance of the cooperatives, agents choose whether or not to remain in the risk-sharing agreement. We highlight the key role of other-regarding preference (altruism and inequality aversion) in stabilizing less segregated (and smaller) cooperatives. Limited knowledge and learning of own risk exposure also contributes to reducing segregation, the two effects (of learning and other-regarding preferences) being complementary. Our findings shed light on the mechanisms behind risk-sharing agreements between agents heterogeneous in their risk exposure.

Xiang Hu Bao (XHB), meaning 'mutual treasury' in Chinese, is a novel online mutual aid platform operated by Alibaba's Ant Financial to facilitate mutual risk sharing of critical illness exposures. XHB reached nearly 100 million members in less than one year since its launch and so far has offered its members critical illness protections at significantly lower cost than traditional critical illness insurance. There are three major distinctions between XHB and traditional insurance products. First, XHB leverages the tech giant's platform and digital technology to lower enrollment and claim processing costs. Second, different from insurance applying sophisticated actuarial pricing models, XHB collects no premiums ex ante from members, but instead equally allocates indemnities and administrative costs among participants after each claims period. Third, XHB limits coverage amount, often below critical illness insurance products, particularly for older participants. We show this restriction potentially leads to separating equilibrium, a la Rothschild-Stiglitz, where low-risk individuals enroll in XHB while high-risk individuals purchase critical illness insurance. Data shows that the incidence rate of the covered illness among XHB members is well below that of comparable critical illness insurance. Our findings further suggest the role of advantageous selection in explaining the cost advantages of the Fintech-based mutual aid programs.

In this paper, we discuss optimal design for stylized Intergenerational Risk Sharing (IRS) pension plans. We study an IRS plan under which both contributions and pension benefits are adjusted based on the level of pension assets. Our optimization focuses on the stability of members’ lifetime consumption, both in the contribution and benefit phases, through formulating the optimization as an ergodic control problem. We illustrate the drawbacks of unconstrained optimization and demonstrate the importance of including regulatory requirements for the sake of fairness across generations. In this formulation, the employers are not included; implicitly, it is assumed that employer contributions would be paid as salary to the workers if not required for the plan, so the employer risk is eliminated.

We show theoretically that the presence of basis risk in index insurance makes it a complement to informal risk sharing, implying that index insurance crowds-in risk sharing and leading to a prediction that demand will be higher among groups of individuals that can share risk. We report results from rural Ethiopia from a first attempt to market weather insurance products to existing informal risk-sharing groups. The groups were offered training on risk management and the possible benefits of holding insurance. Among those trained we randomized the content of training, with some sessions focusing on the benefits of informally sharing basis risk. Our results suggest benefits from marketing index-based insurance with an emphasis on informally sharing basis risk, at least in terms of uptake. Specifically, and consistent with learning informed by the theoretical results, we found that members of groups whose leaders had received training that emphasized risk-sharing had considerably higher uptake.

Insurance sharia based on the cooperation, responsibities, guarantees, protection and assistance among groups of participants. Islamic Insurance (takaful) is considered as cooperative or mutual insurance, where members contribute to pay sum of money or premiums to insurance companies. This study aims to find out the application of Islamic insurance in Indonesia after the law namber 40 of 2014 concerning insurance. This type of research is librabry research. Primary data used are law Number 40 of 2014 corcerning insurance, law number 2 of 1992 KUHD and DSN-MUI fatwa. While the secondary data used is other literature in accordance with the research. The results of this study are summarized as follows: (1) Sharia insurance is an effort to help one another among a number of people/parties through investments in asset and/tabarru‟ which periode a pattern of returns to deal with certain risks through an agreement in accordance with sharia, with a risk sharing system. (2) The authenticity of sharia insurance in Indonesia is needed by strengthening all Islamic insurance products to run in accordance with sharia privisions, in this case the sharia supervisiory board is an important part in carrying out strict supervision of the activities of sharia insurance institutions. Islamic insurance is a solution to answer Muslim needs for the importance of future planning with halal transactions.

In this article we consider the problem of allocating microcredit among a set of networked cooperating agents by a social planner. Network structure, risk aversion and risk sharing of the borrowers have been analyzed in the context of microfinance. We propose a partial liability model, where the borrowers need to take responsibility in case of defaults by their immediate connected neighbours, by committing guarantees as social collateral ex ante to the social planner. We have developed a utility-based allocation model that is Pareto optimal and maximizes a social welfare function. The methodology computes the guarantees and the allocations for the borrowers. We show that the allocation formula for arbitrarily connected networks captures the notion of dominance over neighbours which are one hop away. We also show how the synergy between connectivity, risk aversion and guarantees impacts allocation. We develop the properties of the rule and illustrate them with suitable examples.

Groups of agents, such as participants in a collective pension fund, can decide to undertake a joint investment and to define, ex ante, a rule for the division of proceeds. The collective investment decision and the allocation rule together form a risk sharing scheme. Such a scheme defines a contingent claim for each participant. Given a proposed risk sharing scheme and an agreed-upon pricing functional, the values of these claims can be determined and can be compared to the values of the contributions made by the agents. A risk sharing scheme is said to be financially fair if, for each agent, the value of the agent’s claim as defined by the scheme is equal to the value of the agent’s contribution. The paper provides conditions under which there exists a unique risk sharing scheme that is both Pareto efficient (in the sense of expected utility) and financially fair. Furthermore, an iterative algorithm is presented by which this scheme can be computed. The theory is illustrated by a simple example which shows that, in an incomplete financial market, agents may benefit substantially from forming a collective.

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools.

We provide empirical evidence that Rwandans use the mobile phone network to transfer airtime to those affected by unexpected shocks. Using an extensive dataset on mobile phone activity in Rwanda and exploiting the quasi-random timing and location of natural disasters, we show that individuals make transfers and calls to people affected by disasters. The magnitude of these transfers is small in absolute terms, but statistically significant; in response to the Lake Kivu earthquake of 2008, we estimate that roughly US$84 in airtime was transferred to individuals in the affected region, that 70% of these transfers were immediately used to make outgoing calls, and that US$16,959 was spent calling those near the epicenter. Unlike other forms of interpersonal transfers, mobile airtime is sent over large geographic distances and in response to covariate shocks. Transfers are more likely to be sent to wealthy individuals, and are sent predominantly between pairs of individuals with a strong history of reciprocal favor exchange.

We introduce a new pension product that offers retirees the opportunity for a lifelong income and a bequest for their estate. Based on a tontine mechanism, the product divides pension savings between a tontine account and a bequest account. The tontine account is given up to a tontine pool upon death while the bequest account value is paid to the retiree's estate. The values of these two accounts are continuously re-balanced to the same proportion, which is the key feature of our new product. Our main research question about the new product is what proportion of pension savings should a retiree allocate to the tontine account. Under a power utility function, we show that more risk averse retirees allocate a fairly stable proportion of their pension savings to the tontine account, regardless of the strength of their bequest motive. The proportion declines as the retiree becomes less risk averse for a while. However, for the least risk averse retirees, a high proportion of their pension savings is optimally allocated to the tontine account. This surprising result is explained by the least risk averse retirees seeking the potentially high value of the bequest account at very old ages., 40 pages, 23 pictures. Insurance: Mathematics and Economics(2019)

This paper investigates whether and how the crowding-out effect of formal insurance on informal risk sharing is mitigated by social preference change. We design a lab experiment in which formal insurance is introduced and removed unexpectedly in a repeated risk-sharing game. We find evidence of social preference change by showing that informal risk sharing is significantly improved after the removal of formal insurance, and the pattern mainly occurs when one subject obtains insurance but the other does not. Findings suggest that it is the insurance purchasers who take the initiative to share more risk for their partners. However, there is no significant improvement in informal risk sharing when insurance purchasing decisions are randomly computer generated. We propose a model based on guilt aversion to explain our findings.

Many countries rely on social health insurance supplied by competing insurers to enhance fairness and efficiency in healthcare financing. Premiums in these settings are typically community rated per health plan. Though community rating can help achieve fairness objectives, it also leads to a variety of problems due to risk selection, that is, actions by consumers and insurers to exploit “unpriced risk” heterogeneity. From the viewpoint of a consumer, unpriced risk refers to the gap between her expected spending under a health plan and the net premium for that plan. Heterogeneity in unpriced risk can lead to selection by consumers in and out of insurance and between high- and low-value plans. These forms of risk selection can result in upward premium spirals, inefficient take-up of basic coverage, and inefficient sorting of consumers between high- and low-value plans. From the viewpoint of an insurer, unpriced risk refers to the gap between his expected costs under a certain contract and the revenues he receives for that contract. Heterogeneity in unpriced risk incentivizes insurers to alter their plan offerings in order to attract profitable people, resulting in inefficient plan design and possibly in the unavailability of high-quality care. Moreover, insurers have incentives to target profitable people via marketing tools and customer service, which—from a societal perspective—can be considered a waste of resources. Common tools to counteract selection problems are risk equalization, risk sharing, and risk rating of premiums. All three strategies reduce unpriced risk heterogeneity faced by insurers and thus diminish selection actions by insurers such as the altering of plan offerings. Risk rating of premiums also reduces unpriced risk heterogeneity faced by consumers and thus mitigates selection in and out of insurance and between high- and low-value plans. All three strategies, however, come with trade-offs. A smart blend takes advantage of the strengths, while reducing the weaknesses of each strategy. The optimal payment system configuration will depend on how a regulator weighs fairness and efficiency and on how the healthcare system is organized.

This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being more favorably priced for the policyholders., SCOPUS: ar.j, info:eu-repo/semantics/published

Traditional drug payment schemes in Catalonia are generally based on the negotiation of fixed prices; however, disadvantages arise in the case of innovative therapies. Risk sharing agreements distribute potential health and economic uncertainties and high prices on access across the interested parts. (...)

Previous papers have tested e‐cient risk sharing under the assumption of identical risk preferences. In this paper we show that, if in the data households have heterogeneous risk preferences, the tests proposed in the past reject e‐ciency even if households share risk e‐ciently. To address this issue we propose a method that enables one to test e‐ciency even when households have difierent preferences for risk. The method is composed of three tests. The flrst one can be used to determine whether in the data under investigation households have homogeneous risk preferences. The second and third test can be used to evaluate e‐cient risk sharing when the hypothesis of homogeneous risk preferences is rejected. We use this method to test e‐cient risk sharing in rural India. Using the flrst test, we strongly reject the hypothesis of identical risk preferences. We then test e‐ciency with and without the assumption of preference homogeneity. In the flrst case we reject e‐cient risk sharing at the village and caste level. In the second case we still reject e‐ciency at the village level, but we cannot reject this hypothesis at the caste level. This flnding suggests that the relevant risk-sharing unit in rural India is the caste and not the village.

This paper considers a long-term relationship between two agents who both undertake an action or investment that produces a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. Agents have quasi-linear preferences. Two cases are considered: where agents are risk averse but where limited liability constraints do not bind, and where agents are risk neutral and subject to limited liability constraints. We ask how to structure the investments and division of the surplus over time to avoid expropriation. In the risk-averse case, the dynamics of actions and surplus may or may not be monotonic depending on whether or not a first-best allocation can be sustained. Agents may underinvest but never overinvest. If the first-best allocation is not sustainable, there is a trade-off between risk sharing and surplus maximization; surplus may not be at its constrained maximum even in the long run and the “amnesia” property of pure risk-sharing models fails to hold. In contrast, in the risk-neutral case there may be an initial phase in which one agent overinvests and the other underinvests. Both actions and surplus converge monotonically to a stationary state, where surplus is maximized subject to the self-enforcing constraints.

Intelligent building of EPC mode in domestic development was still in the stage of exploration, and intelligent EPC mode in our country's relevant laws and regulations is not perfect, the most used type of contract of fixed price contract, the employer will most of the risk transfer to the contractor, and through a clause in the contract agreement, not to price adjustment. The contractor can make fewer claims, so the contractor is more likely to have economic losses and longer periods. The root of claim management is how to allocate the risk properly. To assume the risk of the consequences of owner, the contractor can be put in a claim to the, is the key to solve and identify risks shall be borne by the owner, through the analysis of different types of claims, claims evidence library, provide the basis for the reasonable claim.

We consider a matching model in which individuals belonging to two populations (‘males’and ‘females’) can match to share their exogenous income risk. Within each population, individuals can be ranked by risk aversion in the Arrow-Pratt sense. The model permits non transferable utility, a context in which few general results have previously been derived. We show that in this framework (i) a stable matching always exists, (ii) it is essentially unique, and (iii) it is negatively assortative: for any two couples, the more risk averse male is matched with the less risk averse female. We discuss the implications of these results for the empirical analysis of risk-sharing.