随机利率与随机波动率模型下保险公司的均衡 再保险-投资策略

This paper considers the equilibrium reinsurance-investment strategy under stochastic interest rate and stochastic volatility models. The surplus process of the insurer is assumed to follow a Brownian motion with drift, and the insurer can purchase proportional reinsurance or acquire new business. Moreover, it is allowed to invest in a financial market consisting of a bank account, a bond and a risky asset. Particularly, the interest rate is stochastic and characterized by the Cox-Ingersoll-Ross model, while the price process of the risky asset is described by the Heston model. By applying stochastic control theory and solving an extended Hamilton-Jacobi-Bellman equation, we obtain the equilibrium reinsurance-investment strategy and the corresponding value function explicitly. Finally, some numerical illustrations are provided to show the impacts of model parameters on the equilibrium strategy.