Robust reinsurance strategy under ambiguity-averse

Abstract

In this paper, we study the robust optimal reinsurance policy for an insurer with ambiguity aversion in the continuous time model within a class of mixed reinsurance premium criteria, under which several common premium criteria are included.By minimizing the discounted ruin probability of the insurer and maximizing the expected wealth utility of the insurer at the terminal moment, the explicit expressions of the value function and the corresponding robust optimal reinsurance strategy are obtained in both the Cramér-Lundberg jump model and its diffusion approximation model.For the optimization problem of minimizing the discounted ruin probability of the insurer, we prove that the value function has the exponential form by giving an equivalent form of the value function of the optimization problem.In addition, to solve the optimization problems, we construct the auxiliary Lagrangian function of the optimizationproblem skillfully, and then explicitly obtain the expression of robust optimal reinsurance strategy under the general mixed reinsurance criteria.It turns out that the optimal reinsurance strategy has a non trivial structure in the form of curve, which is very different from piecewise linear reinsurance strategy (such as proportional reinsurance strategy, excess loss reinsurance strategy and layer reinsurance strategy). This greatly enriches the results of optimal reinsurance. Finally, we show the sensibilities of some model parameters (including ambiguity-aversion level) to the optimal reinsurance strategy and value function.