Mean-Variance Investment and Reinsurance Optimization with Stochastic Interest Rate and Volatility

Abstract

This paper studies a continuous-time investment and reinsurance problem for an insurer. The financial market consists of one money market asset, one stock, and two zero-coupon bonds. Interest rates follow a generalized Cox-Ingersoll-Ross model, and the stock price is given by the Heston stochastic volatility model, with the stochastic interest rate and volatility processes being correlated. The insurer purchases proportional reinsurance to mitigate its risk and invests the surplus in the financial market, with the purpose to optimize mean-variance preferences in the precommitment sense. By the theory of backward stochastic differential equations and linear-quadratic control, the insurer's efficient strategy and efficient frontier are both obtained in closed form. An empirical analysis using market data validates the proposed financial model, and a numerical study offers valuable insights into the impact of model inputs on the insurer's efficient frontier.