Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets

TL;DR

This paper develops a stochastic control model for an insurance company's optimal reinsurance and investment strategies considering common shocks affecting both claims and financial markets, with solutions derived via PDEs.

Contribution

It introduces a model incorporating environmental factors and common shocks into reinsurance and investment optimization, providing explicit strategies and a comparison analysis.

Findings

Optimal strategies characterized through PDE solutions

Common shocks significantly influence reinsurance and investment decisions

Model captures joint impact of catastrophic events on financial and insurance risks

Abstract

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 model 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 the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we provide a verification result for the value function via classical solutions to two backward partial differential equations and characterize the optimal reinsurance and investment strategies. Finally, we make a comparison analysis to discuss the effect of common shock dependence.