Optimal Investment for an Insurer to Minimize Its Probability of Ruin

TLDR

The model extends Hipp and Plum (2000) by incorporating a risk‑free asset. The paper studies optimal investment strategies for an insurance company. Premium income is modeled as a constant rate, claims as a compound Poisson process, and the insurer can invest in a risk‑free asset and a risky stock; the authors numerically solve the resulting Hamilton–Jacobi–Bellman equation for various claim‑size distributions, analyze the influence of parameters such as stock volatility, and extend the framework to include borrowing constraints or reinsurance. The results provide managerial insights into optimal investment decisions for insurers.

Abstract

Abstract This paper studies optimal investment strategies of an insurance company. We assume that the insurance company receives premiums at a constant rate, the total claims are modeled by a compound Poisson process, and the insurance company can invest in the money market and in a risky asset such as stocks. This model generalizes the model in Hipp and Plum (2000) by including a risk-free asset. The investment behavior is investigated numerically for various claim-size distributions. The optimal policy and the solution of the associated Hamilton-Jacobi-Bellman equation are then computed under each assumed distribution. Our results provide insights for managers of insurance companies on how to invest. We also investigate the effects of changes in various factors, such as stock volatility, on optimal investment strategies, and survival probability. The model is generalized to cases in which borrowing constraints or reinsurance are present.