Safety-first criterion of security portfolio selection in jump-diffusion market for insurer

This paper discusses the optimal constant rebalanced portfolio choice problem of an insurer under the safety-first criterion. The surplus process of the insurer is assumed to follow the Cramer–Lundberg model. The insurer invests its surplus in a financial market, which consists of one risk-free bond and n risky assets, whose prices follow an n-dimensional jump-diffusion process. Using the safety-first criterion as a measure of the overall risk of the insurer, we explore the problem of selecting the optimal investment strategy for an insurer under the constraints of acceptable disaster levels. The martingale integral property is used to transform the dynamic problem into a static one, and explicit expressions for the optimal investment strategy are obtained. Based on this, the impact of factors such as disaster level, claim intensity, premium rate and claim size on the optimal investment strategy is analyzed, and some economic explanations are given. Finally, actual data from financial markets are used to simulate how insurance companies allocate investment funds.