Optimal reinsurance and investment problem with default risk and bounded memory

This paper considers an insurer with constant absolute risk aversion (CARA) preference and explores a reinsurance-investment optimisation problem where the insurer 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 savings account, a defaultable corporate zero-coupon bond and a risky asset with constant elasticity of variance (CEV) stochastic volatility. The problem is modelled using a stochastic system with delay. Under certain conditions, the analytic optimal reinsurance-investment policy is derived, and the corresponding verification theorem is provided. Finally, a sensitivity analysis is conducted 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.