Pareto-optimal reinsurance under dependence uncertainty

Abstract

This paper studies Pareto-optimal reinsurance design in a monopolistic market with multiple primary insurers and a single reinsurer, all with heterogeneous risk preferences. The risk preferences are characterized by a family of risk measures, called Range Value-at-Risk (RVaR), which includes both Value-at-Risk (VaR) and Expected Shortfall (ES) as special cases. Recognizing the practical difficulty of accurately estimating the dependence structure among the insurers' losses, we adopt a robust optimization approach that assumes the marginal distributions are known while leaving the dependence structure unspecified. We provide a complete characterization of optimal indemnity schedules under the worst-case scenario, showing that the infinite-dimensional optimization problem can be reduced to a tractable finite-dimensional problem involving only two or three parameters for each indemnity function. Additionally, for independent and identically distributed risks, we exploit the argument of asymptotic normality to derive optimal two-parameter layer contracts. Finally, numerical applications are considered in a two-insurer setting to illustrate the influence of the dependence structures and heterogeneous risk tolerances on optimal strategies and the corresponding risk evaluation.

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