Optimal Proportional Reinsurance To Reach A Goal For The Risk Model With Common Shock Dependence

This paper studies an optimal reinsurance problem with two dependent classes of insurance business,where the two claim number processes are correlated through a common shock.Assume that the insurer's surplus process is modulated by the diffu-sion process which is an approximation of the classical Cramer-Lundberg model,and she/he can purchase proportional reinsurance and invest her/his surplus in a risk-free asset.Two optimization problems,namely maximizing/minimizing the expected time and maximizing/mimmizing the probability of hitting a target before default,are con-sidered.Using the technique of dynamic programing principle,explicit expressions,not only for the optimal strategy but also for the value function,are derived for the two optimization problems.We find that the value function of the two optimization problems depends on the barrier.Finally,some numerical examples are presented to show the impact of model parameters on the optimal results.