Optimal reinsurance-investment strategy in a stochastic financial market

Insurance company can purchase proportional reinsurance to hedge the risk of insurance. Meantime, insurance company can invest its wealth into the financial market to preserve or increase the value. In this paper, surplus process is supposed to be driven by Brownian motion with drift, short rate is described by stochastic affine interest rate model and the volatility of stock price is governed by Heston's stochastic volatility model. By using the technique of stochastic dynamic programming and Hamilton-Jocabi-Bellman (HJB) equation, optimal reinsurance-investment strategy with exponential utility is obtained in explicit form. A numerical example is given to analyze the sensitivity of optimal reinsurance-investment strategy to model parameters. Research results display that optimal reinsurance strategy does not only depend on the parameters of insurance market, but also depends on the parameters of financial market; optimal reinsurance -investment strategies with stochastic interest rate and stochastic volatility are closely related to the dynamics of interest rate and have nothing to do with the dynamics of volatility; the reinsurance behavior has no effect on the amount in the stock, yet has a considerable influence on the amount in the zero-coupon bond. © 2019, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.