We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.

Network mutual aid platforms is one of the popular risk-sharing models in recent years, and they have almost 200 million members in China. However, current mutual aid platforms does not satisfy the actuarial rules in either the apportionment method or the pricing principle. Hence, a variety of mutual aid models which enable mutual aid members with different risks to exchange their risks in a transparent and actuarial fair way have been proposed in this paper. Besides, the decision-making frameworks for participants choosing between the mutual aid platform and similar insurance products, or choosing no risk sharing are constructed, respectively. Decisions are made based on the principle of maximizing expected utility. Moreover, the optimization problems of maximizing profit and minimizing risk are constructed, respectively. Through the principle of individual fairness and relative fairness, the problem of adverse selection of the platform can also be reduced. Finally, the actual mutual aid plan is compared with similar insurance products to discuss the advantages of the optimized plan.

This paper studies bilateral risk sharing under no aggregate uncertainty, where one agent has Expected-Utility preferences and the other agent has Rank-dependent utility preferences with a general probability distortion function. We impose exogenous constraints on the risk exposure for both agents, and we allow for any type or level of belief heterogeneity. We show that Pareto-optimal risk-sharing contracts can be obtained via a constrained utility maximization under a participation constraint of the other agent. This allows us to give an explicit characterization of optimal risk-sharing contracts. In particular, we show that an optimal risk-sharing contract contains allocations that are monotone functions of the likelihood ratio, where the latter is obtained from Lebesgue’s Decomposition Theorem.

We present an analysis of interregional consumption risk sharing in Russia between 1999 and 2009 using novel estimation methods. In addition to standard fixed-effects panel estimations, we use system and difference GMM estimators to reflect time dynamic properties and possible endogeneity between output and consumption. Furthermore, we apply spatial models that control for spatial dependence across regions. The results show that regional consumption deviations from the national average are highly persistent in time and space. Nevertheless, the regional consumption risk sharing in Russia is relatively high with 70%–90% of idiosyncratic risk being smoothed. Finally, fiscal policy and the degree of financial development appear to contribute to the consumption smoothing.

In a risk exchange, participants trade a privately owned risk for a share in a pool. If participants agree on a valuation rule, it can be decided whether or not, according to the given rule, these trades take place at equal value. If equality of values holds for all participants, then the exchange is said to be “financially fair”. It has been shown by Bühlmann and Jewell (1979) that, under mild assumptions, the constraint of financial fairness singles out a unique solution among the set of all Pareto efficient risk exchanges. In this paper, we find that an analogous statement is true if we limit ourselves to linear exchanges. Conditions are provided for existence and uniqueness of linear sharing rules that are both financially fair and Pareto efficient among all linear sharing rules. The performance of the linear rule is compared to that of the general (nonlinear) rule in a number of specific cases.

This paper studies optimal risk redistribution between firms, such as institutional investors, banks or insurance companies. We consider the case where every firm uses dual utility (also called a distortion risk measure) to evaluate risk. We characterize optimal risk redistributions via four properties that need to be satisfied jointly. The characterized risk redistribution is unique under three conditions. Whereas we characterize risk redistributions by means of properties, we can also use some results to study competitive equilibria.We characterize uniqueness of the competitive equilibrium in markets with dual utilities. Finally, we identify two conditions that are jointly necessary and sufficient for the case that there exists a trade that is welfare-improving for all firms.

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 a typical equity-linked life insurance contract, the insurance company is entitled to a share of return surpluses as compensation for the return guarantee granted to the policyholders. The set of possible contract terms might, however, be restricted by a regulatory default constraint — a fact that can force the two parties to initiate sub-optimal insurance contracts. We show that this effect can be mitigated if regulatory policy is more flexible. We suggest that the regulator implement a traffic light system where companies are forced to reduce the riskiness of their asset allocation in distress. In a utility-based framework, we show that the introduction of such a system can increase the benefits of the policyholder without deteriorating the benefits of the insurance company. At the same time, default probabilities (and thus solvency capital requirements) can be reduced.

Objectives: This study assesses the use of routinely collected claims data for managed entry agreements (MEA) in the illustrative context of German statutory health insurance (SHI) funds.

Methods: Based on a nonsystematic literature review, the data needs of different MEA were identified. A value-based typology to classify MEA on the basis of these data needs was developed. The typology is oriented toward health outcomes and utilization and costs, key components of a new technology's value. For each MEA type, the suitability of claims data in establishing evidence of the novel technology's value in routine care was systematically assessed. Assessment criteria were data availability, completeness, timeliness, confidentiality, reliability, and validity.

Results: Claims data are better suited to MEA addressing uncertainty regarding the utilization and costs of a novel technology in routine care. In schemes where safety aspects or clinical effectiveness are assessed, the role of claims data is limited because clinical information is not included in sufficient detail.

Conclusions: The suitability of claims data depends on the source of uncertainty and, in consequence, the outcome measures chosen in the agreements. In all schemes, the validity of claims data should be judged with caution as data are collected for billing purposes. This framework may support manufacturers and payers in selecting the most suitable contract type and agreeing on contract conditions. More research is necessary to validate these results and to address remaining medical, economic, legal, and ethical questions of using claims data for MEA.

In this paper, I analyze an optimal loan contract between a risk-neutral financial intermediary and a risk-averse household, where the household receives a stochastic endowment stream that grows over time and is unable to commit to the contract. I examine the household's welfare in the equilibrium contract, and find that, first, under sufficiently rapid endowment growth, the presence of uncertainty in endowment may improve the household's welfare through relaxation of its commitment problem, and second, regardless of the endowment growth rate, the household's welfare is nonincreasing in the persistence of endowment. Numerical analysis suggests that welfare improvement from uncertainty may occur under reasonable parameters. These results have potentially important practical implications—for example, for developing countries that rely on external borrowing.

With the current sovereign debt crisis, the incompleteness of economic integration in the Economic and Monetary Union (EMU) has become patent, leading to an intense debate among academics and policy makers. Much of the debate concerns fiscal rules and austerity measures, both of which weigh on growth prospects. In this paper we look at the main structural shortcomings of EMU through the lens of general equilibrium theory. We address two issues (international sharing of macroeconomic risks and coordinated growth stimulation) which are at the heart of the sustainability of EMU. We propose: (A) a specific scheme for mutual insurance of macroeconomic risks; (B) locating responsibility for demand policies at the EMU level, with ambitious investment programs (public, or fiscally-neutral private) as main instrument.

We study the microeconomic and macroeconomic effects of longevity insurance. Using a tractable discrete-time overlapping-generations model of a closed economy we first study different types of government redistribution of accidental bequests in general equilibrium. Individuals face longevity risk, as there is a positive probability of passing away before the retirement period. We find nonpathological cases where it is better for long-run welfare to waste accidental bequests than to give them to the elderly. Next we study the introduction of a perfectly competitive life insurance market offering actuarially fair annuities. There exists a tragedy of annuitization: although full annuitization of assets is privately optimal, it is not socially beneficial, because of adverse general equilibrium repercussions.

In a defined contribution pension system, one of the main risks faced by members refers to the investment of funds. In this context, we discuss which is the most suitable risk measurement for the affiliates to the pension system. Different life-cycle investment strategies are evaluated under this measure for different types of workers. We point out the importance of designing well-suited default investment options in light of the economic behavior of members, characterized by low financial knowledge, inertia and myopia in decision-making. We calibrate a pension risk model for the Chilean economy, including measures of life-cycle income, human capital risk, investment and annuitization risks. Our results suggest that affiliates can gain (loss) around 0.85 percentage points in terms of average replacement rates in return for an increase (decrease) of 1 percentage point in risk, measured as standard deviation of replacement rates. Using a stochastic dominance analysis, we find that there are no dominated strategies when subsidies from the Solidarity Pillar are excluded. When the Solidarity Pillar is considered, the most appropriate investment strategies for affiliates that receive these subsidies are concentrated on the riskier funds. However, this also means that there could be increased pressure on Government spending in order to grant additional benefits to affiliates. Our model has a wide range of practical applications that go from informing affiliates about the degree of uncertainty associated to their expected replacement rate to a guide to evaluate how different investment strategies affect the expected values of affiliates' pensions and their associated risk.

The asset allocation is a crucial decision for pension funds, and this paper analyses the economic factors which determine this choice. The analysis proceeds on the basis that, in the absence of taxation, risk sharing and default insurance, the asset allocation between equities and bonds is indeterminate and governed by the risk/return preferences of the trustees and the employer. If the employing company and its shareholders are subject to taxation, there is a tax advantage in a largely bond allocation. Risk sharing between the employer and the employees often means that one group favours a high equity allocation, while the other favours a low equity allocation. Underpriced default insurance creates an incentive for a high equity allocation. When taxation, risk sharing and underpriced default insurance are all present, it is concluded that the appropriate asset allocation varies with the circumstances of the scheme; but that a high equity allocation is probably inappropriate for many private sector pension schemes.

The paper examines a classical risk model where both insurance and reinsurance policies are chosen by the insurer in order to minimize the expected maximal loss. We show that the optimal control problem reduces to a static case. We found that the optimal reinsurance is excess of loss reinsurance and describe the set optimal insurance policies. Such a policy providing the minimal variance of the risk left with insured turns out to be a combination of stop loss and deductible policies. The results are illustrated by two numerical examples.