Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with more General Dependent Claim Risks and Defaultable Risk

This paper is devoted to investigating a robust optimal excess-of-loss reinsurance and investment problem with defaultable risk, in which the insurer’s wealth process is described by a more general dependent risk model with two classes of insurance business. The insurer is allowed to purchase excess-of-loss reinsurance and invest in a risk-free asset, a defaultable bond and a risky asset whose price depends on a square-root stochastic factor process which makes the geometric Brownian motion, CEV model and Heston model as special cases. Our aim is to seek the optimal excess-of-loss reinsurance and investment strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. Applying the stochastic control theory, the robust Hamilton-Jacobi-Bellman (HJB) equations for the post-default case and the pre-default case are first established, respectively. Then the explicit expressions of the optimal control strategy are obtained, moreover, we provide the verification theorem. Finally, some numerical examples are given to illustrate our results.