摘要
假设保险公司的盈余过程由跳扩散风险模型来刻画。为了保值增值,保险公司购买超额损失再保险来降低自身风险,同时将其盈余投资于金融市场中的无风险资产和风险资产。其中,无风险资产的利率服从Vasicek利率模型,风险资产价格遵循CEV模型。保险公司的目标是终端财富的期望指数效用最大化。接着,应用随机最优控制的方法建立了值函数相应的HJB方程,并在指数效用函数下求解得到最优策略。最后,运用数值算例方法阐述了模型参数对最优策略的影响。研究结果说明风险厌恶系数和利率风险对最优策略的影响较大。
Assume that the earnings process of an insurance company is described by the jump-diffusion risk model.In order to preserve and increase value,the insurance company purchases excess loss reinsurance to reduce its risk while investing its surplus in risk-free and risky assets in the financial market.Among them,the interest rate of risk-free assets follows the Vasicek interest rate model,and the price of risk assets follows the Constant Elasticity of Variance(CEV)model.The insurance company aims to maximize the expected exponential utility of terminal wealth.Then,the Hamilton-Jacobi-Bellan(HJB)equation corresponding to the value function is established with the method of stochastic optimal control,and the optimal strategy is obtained by solving the equation under the exponential utility function.Finally,the influence of model parameters on the optimal strategy is illustrated by numerical examples.The results show that the risk aversion coefficient and interest rate risk greatly influence the optimal strategy.
作者
徐文静
夏登峰
杨铭
韩雪伟
XU Wenjing;XIA Dengfeng;YANG Ming;HAN Xuewei(School of Mathematics,Physics and Finance,Anhui Polytechnic University,Wuhu 241000,China)
出处
《安徽工程大学学报》
2025年第3期63-70,共8页
Journal of Anhui Polytechnic University
基金
安徽省高校自然科学研究重点项目(KJ2021A0514)。
关键词
超额损失再保险
随机利率
跳-扩散模型
CEV模型
HJB方程
excess loss reinsurance
stochastic interest rate
jump-diffusion model
Constant Elasticity of Variance model
Hamilton-Jacobi-Bellman equation
