Optimal reinsurance and investment under common shock dependence between financial and actuarial markets

We study optimal proportional reinsurance and investment strategies for an insurance company which experiences both ordinary and catastrophic claims and wishes to maximize the expected exponential utility of its terminal wealth. We propose a modeling setting where the insurance framework is affected by environmental factors, and aggregate claims and stock prices are subject to common shocks, i.e. drastic events such as earthquakes, extreme weather conditions, or even pandemics, that have an immediate impact on the financial market and simultaneously induce insurance claims. Using a classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we provide a verification result for the value function via classical solutions of two backward partial differential equations and characterize the optimal reinsurance and investment strategy. Finally, we provide a comparison analysis to discuss the effect of common shock dependence.