Optimal reinsurance and investment problem for an insurer with counterparty risk

This paper analyzes the optimal proportional reinsurance and investment problem for an insurer in a defaultable market. We assume that the reinsurance premium is calculated via the exponential premium principle. The insurer can allocate his/her wealth among the following securities: a bank account, a risky stock asset and a corporate bond. We decompose the original optimization problem into two sub-problems: a pre-default case and a post-default case. The optimal reinsurance and investment policies that maximize the expected CARA utility of the terminal wealth are explicitly derived. Numerical examples are given to illustrate our results, and we discuss relevant economic insights obtained from these results.