Optimal reinsurance-investment problem with default risk for an insurer under the constant elasticity of variance model.

This article investigates the optimal reinsurance and investment strategies for an insurer with constant absolute risk aversion (CARA) utility, considering proportional reinsurance and investments in a risk-free bond, a stock following the constant elasticity of variance (CEV) model, and a defaultable bond. The study incorporates the correlation between the insurer’s risk process and the stock price, as well as default risk associated with the bond investment. By solving the Hamilton–Jacobi–Bellman (HJB) equation, explicit optimal strategies are derived for both pre-default and post-default scenarios, revealing that default risk does not affect the optimal stock investment or reinsurance strategies, while the stock’s volatility and its correlation with the risk process significantly influence these strategies. Numerical analyses illustrate how model parameters such as correlation, risk aversion, and credit spreads impact the insurer’s optimal decisions, providing practical insights for managing insurance and financial risks in the presence of defaultable assets.