Time-consistent investment-proportional reinsurance strategy under a jump-diffusion model

Abstract

In this paper, we formulate a mean-variance portfolio selection problem of an insurer who manages her underlying risk by purchasing proportional reinsurance and investing in a financial market consisting of a bank account and a risky asset following a jump-diffusion dynamics with random parameters. We then obtain a time-consistent equilibrium strategy via a flow of Backward Stochastic Differential Equations. Finally, we apply our results to a mean-reverting Levy-Ornstein-Uhlenbeck process and obtain closed form solutions.