Optimal Risk Sharing in Society

We consider risk sharing among individuals in a one-period setting under uncertainty that will result in payoffs to be shared among the members. We start with optimal risk sharing in an Arrow–Debreu economy, or equivalently, in a Borch-style reinsurance market. From the results of this model we can infer how risk is optimally distributed between individuals according to their preferences and initial endowments, under some idealized conditions. A main message in this theory is the mutuality principle, of interest related to the economic effects of pandemics. From this we point out some elements of a more general theory of syndicates, where in addition, a group of people are to make a common decision under uncertainty. We extend to a competitive market as a special case of such a syndicate.

Asset Pricing With Endogenously Uninsurable Tail Risk

This paper studies asset pricing and labor market dynamics when idiosyncratic risk to human capital is not fully insurable. Firms use long‐term contracts to provide insurance to workers, but neither side can fully commit; furthermore, owing to costly and unobservable retention effort, worker‐firm relationships have endogenous durations. Uninsured tail risk in labor earnings arises as a part of an optimal risk‐sharing scheme. In equilibrium, exposure to the tail risk generates higher aggregate risk premia and higher return volatility. Consistent with data, firm‐level labor share predicts both future returns and pass‐throughs of firm‐level shocks to labor compensation.

BILATERAL RISK SHARING WITH HETEROGENEOUS BELIEFS AND EXPOSURE CONSTRAINTS

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.

On the Optimal Risk Sharing in Reinsurance with Random Recovery Rate

This paper studies a Pareto-optimal reinsurance contract in the presence of negative statistical dependence between the insurance claim and the random recovery rate. In the context of symmetric information model and asymmetric information model, we investigate properties of the Pareto-optimal indemnity schedules. For risk neutral reinsurer with proportional cost and associated expense, we present possible forms of the Pareto-optimal indemnity schedule as well.