Portfolio selection and risk control for an insurer in the Lévy market under mean-variance criterion

In this paper, we apply the martingale approach to investigate the optimal investment and risk regulation problem for an insurer. Assume that the insurer is allowed to invest in a financial market consisting of one risk-free asset and one risky asset whose price is modeled by a Lévy process. The risk process of the insurer is described by another Lévy process, and the insurer can regulate the risk by controlling the number of insurance polices. Finally, the closed-form expressions for the efficient strategy and efficient frontier are given under the criterion of mean-variance.