基于Heston’s SV模型下带有违约风险的最优再保险—投资策略

对于模糊厌恶型保险公司,在可违约金融市场中,考虑其比例再保险—投资问题。假设在任意时刻保险公司可购买比例再保险和投资无风险资产、风险资产和可违约债券,其中风险资产价格服从Heston’s SV(Heston s Stochastic Volatility)模型。首先,考虑模型不确定性,采用与参考模型概率测度等价的概率测度描述替代模型。利用Girsanov变换得到保险公司在替代模型下的财富过程,并通过动态规划原理建立了相应的HJB(Hamilton-Jacob-Bellman)方程,其中,文章用含状态依赖的不同偏好参数度量模型不确定性的模糊度。其次,分别在违约前和违约后的情况下,针对CARA(Constant Absolute Risk Aversion)效用函数求解HJB方程,得到了最优稳键的再保险—投资策略,并给出了数值模拟和经济学解释。结果表明:相比较使用同一偏好参数的模型结果,文章的最优策略的表达式更精确,考虑的模型更符合实际金融环境。

变利率下基于SV模型的最优再保险-投资研究

对于模糊厌恶型保险商(ambiguity-averse insurer,简称AAI),考虑比例再保险,并将盈余资金在无风险资产和风险资产中进行配置,假设无风险利率是以确定性利率函数表示,而风险资产价格服从Heston随机波动率模型。首先,在模型不确定下,利用Girsanov变换得到保险商的等价财富方程。其次,通过动态规划原理建立了相应的HJB (Hamilton-Jacob-Bellman)方程,并针对CARA (Constant Absolute Risk Aversion)效用函数求解HJB方程,得出最优的再保险-投资策略,最后给出数值模拟并做出经济学解释。

Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsurance to transfer part of the insurance claims risk.In addition to reinsurance,she also can invests her surplus in a financial market,which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility(SV)model.Considering the performance-related capital flow,the insurer’s wealth process is modeled by a stochastic differential delay equation.The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth.We explicitly derive the optimal strategy and the value function.Finally,we provide some numerical examples to illustrate our results.