SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Nian Yao
Abstract. We study the optimal excess-of-loss reinsurance and portfolio for an insurer in a defaultable market by a general stochastic volatility model. The insurer is assumed to 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 through two subproblems: a pre-default case and a post-default case, respectively. 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 policy that maximizes a utility associated with the ]terminal wealth. Verification theorem is established to show the uniqueness of the corresponding solution of HJB equation. Moreover, the portfolio of multiple defaultable corporate bonds and a bank account with reinsurance is also considered.