Optimal reinsurance and investment problem with multiple risky assets and correlation risk for an insurer under the Ornstein-Uhlenbeck model

Abstract

This paper studies the optimal reinsurance and investment problem with multiple risky assets and correlation risk. The claim process is described by a Brownian motion with drift. The insurer is allowed to invest in a risk-free asset and multiple risky assets and the instantaneous return rate of each risky asset follows the Ornstein-Uhlenbeck (O-U) model. Moreover, the correlation between risk model and the risky assets’ price is taken into account. We first consider the optimal investment problem for the insurer. Subsequently, we assume that the insurer can purchase proportional reinsurance and invest in the financial market. In both cases, the insurer’s objective is to maximize the expected exponential utility of the terminal wealth. By applying stochastic control approach, we derive the optimal reinsurance and investment strategies and the corresponding value functions explicitly. Finally, numerical simulations are presented to illustrate the effects of model parameters on the optimal reinsurance and investment strategies.

Keywords:

• Investment for an insurer
• reinsurance
• Ornstein-Uhlenbeck model
• multiple risky assets
• correlation risk
• dynamic programming

Additional information

Funding

The authors are very grateful to the anonymous referees for their insightful comments and helpful suggestions. This research was supported by National Natural Science Foundation of China (Grant Nos. 11871052, 11771329, 12171360), Key Project of the National Social Science Foundation of China (Grant No. 21AZD071) and Natural Science Foundation of Tianjin City (Grant No. 20JCYBJC01160).