基于Heston’s SV模型下带有违约风险的最优再保险—投资策略

Optimal Reinsurance and Investment Based on Heston’s SV Model in Defaultable Market

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。

For an ambiguity-averse insurer(AAI),the robust optimal reinsurance and investment strategy problem in the defaultable financial market is studied in this research.We assume that the insurer is allowed to purchase proportional reinsurance and to invest on a risk-free asset,a risky asset and a defaultable bond at any time,where the price process of the risky asset follows the Heston s stochastic volatility model.Firstly,in the case of model uncertainty,the probability measure equivalent to the probability measure of the reference model is used to describe the alternative model.The wealth process of the insurer under the alternative model is obtained by Girsanov transformation,and the corresponding Hamilton-Jacob-Bellman equation,which measures the ambiguity degree of model uncertainty with different preference parameters with state dependence,is established by dynamic programming approach.Then,the closed-form expressions of the optimal reinsurance and investment strategy is derived by solving Hamilton-Jacob-Bellman equation with the CARA utility function in the pre-default case and post-default case,respectively.And,the numerical simulation and its economic analysis are given.The results show that,compared with the model results using the same preference parameter,the expression of our optimal strategy is more accurate,and the model considered is more consistent with the actual financial environment.