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In this paper, we study an optimal excess-of-loss reinsurance and investmentproblem for an insurer in defaultable market. The insurer can buy reinsuranceand invest in the following securities: a bank account, a risky asset withstochastic volatility and a defaultable corporate bond. We discuss the optimalinvestment strategy into two subproblems: a pre-default case and a post-defaultcase. We show the existence of a classical solution to a pre-default case viasuper-sub solution techniques and give an explicit characterization of theoptimal reinsurance and investment policies that maximize the expected CARAutility of the terminal wealth. We prove a verification theorem establishingthe uniqueness of the solution. Numerical results are presented in the case ofthe Scott model and we discuss economic insights obtained from these results.

Optimal excess-of-loss reinsurance and investment problem for an insurer with default risk under a stochastic volatility model