Optimal investment-reinsurance policy under a long-term perspective

TL;DR

This paper investigates the long-term optimal investment and reinsurance strategies for an insurer considering interest and inflation risks, deriving explicit solutions and comparing models.

Contribution

It introduces a long-term perspective into the investment-reinsurance problem, deriving closed-form optimal policies considering stochastic interest and inflation risks.

Findings

Closed-form optimal policies derived from Hamilton-Jacobi-Bellman equation.

Verification theorem established without Lipschitz condition.

Numerical analysis compares Ho-lee and Vasicek models.

Abstract

In this paper, we assume an insure is allowed to purchase proportional reinsurance and can invest his or her wealth into the financial market where a savings account, stocks and bonds are available. Different from classical optimal investment and reinsurance problem, this paper studies the insurer's long-term investment decision. Under this setting, our model consider the interest risk and the inflation risk. Specifically, we suppose the interest rate follows a stochastic process, while price index is described by a classical model. By solving Hamilton-Jacobi-Bellman equation, the closed-form expression of the optimal policy is obtained. Further, we prove the corresponding verification theorem without the usual Lipschitz condition. In the end, numerical examples are made to illustrate the difference of the optimal polices under Ho-lee model and Vasicek model.