Optimal excess of loss reinsurance contract with ambiguity aversion in the principal agent model
ABSTRACT We discuss an optimal excess of loss reinsurance contract in a continuous time principal agent framework where the surplus of the insurer (agent/he) is described by a classical Cramer Lundberg (C L) model. In addition to reinsurance, the insurer and the reinsurer (principal/she) are both allowed to invest their surpluses into a financial market containing one risk free asset (e.g. a short rate account) and one risky asset (e.g. a market index) In this paper, the insurer and the reinsurer are ambiguity averse and have specific modeling risk aversion preferences for the insurance claims (this relates to the jump term in the stochastic models) and the financial market's risk (this encompasses the models' diffusion term) The reinsurer designs a reinsurance contract that maximizes the exponential utility of her terminal wealth under a worst case scenario which depends on the retention level of the insurer. By employing the dynamic programming approach, we derive the optimal robust reinsurance contract, and the value functions for the reinsurer and the insurer under this contract. In order to provide a more explicit reinsurance contract and to facilitate our quantitative analysis, we discuss the case when the claims follow an exponential distribution; it is then possible to show explicitly the impact of ambiguity aversion on the optimal reinsurance.
Scandinavian Actuarial Journal