Optimal Excess-of-loss Reinsurance and Investment Problem for an Insurer with Default Risk under a Stochastic Volatility Model

In this paper, we study an optimal excess-of-loss reinsurance and investment problem for an insurer in defaultable market. The insurer can buy reinsurance and invest in the following securities: a bank account, a risky asset with stochastic volatility and a defaultable corporate bond. We discuss the optimal investment strategy into two subproblems: a pre-default case and a post-default case. We show the existence of a classical solution to a pre-default case via super-sub solution techniques and give an explicit characterization of the optimal reinsurance and investment policies that maximize the expected CARA utility of the terminal wealth. We prove a verification theorem establishing the uniqueness of the solution. Numerical results are presented in the case of the Scott model and we discuss economic insights obtained from these results. Keyword: optimal reinsurance · optimal investment · default risk · HamiltonJacobi-Bellman equation · stochastic volatility model. 2010 Mathematical Subject Classification: Primary 93E20; Secondary 60H30