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基于Heston's SV模型下带有违约风险的最优再保险-投资策略
引用本文:陈振龙,苑伟杰,夏登峰.基于Heston's SV模型下带有违约风险的最优再保险-投资策略[J].商业经济与管理,2021,41(5):56-70.
作者姓名:陈振龙  苑伟杰  夏登峰
作者单位:1.浙江工商大学 统计与数学学院
2.安徽工程大学 金融工程系
基金项目:浙江省自然科学基金项目;教育部人文社会科学研究规划基金;国家自然科学基金项目;浙江省重点建设高校优势特色学科(浙江工商大学统计学)
摘    要: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。

关 键 词:模糊厌恶型保险公司  Heston's  SV模型  可违约债券  动态规划原理  稳键的再保险-投资  
收稿时间:2020-12-12

Optimal Reinsurance and Investment Based on Heston's SV Model in Defaultable Market
CHEN Zhenlong,YUAN Weijie,XIA Dengfeng.Optimal Reinsurance and Investment Based on Heston's SV Model in Defaultable Market[J].Business Economics and Administration,2021,41(5):56-70.
Authors:CHEN Zhenlong  YUAN Weijie  XIA Dengfeng
Institution:1.School of Statistics and Mathematics, Zhejiang Gongshang University
2.Department of Financial Engineering, Anhui Polytechnic University
Abstract: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.
Keywords:ambiguity-averse insurer  Heston's SV model  defaultable bond  dynamic programming approach  robust reinsurance and investment  
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