Optimal Reinsurance and Investment Problem With Default Risk and Bounded Memory

This paper considers an insurer with CARA preference and explores an reinsurance-investment optimization problem where the insurer's income is related to the historical wealth performance. The insurer can purchase proportional reinsurance contracts to transfer the claim risk and allocate the remaining liquid wealth in a saving account, a defaultable corporate zero coupon bond and a risky asset with constant elasticity of variance (CEV) stochastic volatility. The problem is modeled using a stochastic system with delay. Under certain condition, the analytic optimal reinsurance-investment policy is derived and the corresponding verification theorem is provided. Finally, we conduct sensitivity analysis on the optimal reinsurance-investment policies over different memory parameters. The results show that longer memory leads to more prudent reinsurance and investment decisions for the insurer