具有共同冲击相依性的跳扩散金融市场中有着延迟和违约风险的鲁棒最优再保险和投资策略  

Robust Optimal Reinsurance and Investment Strategies with Delay and Default Risk in a Jump-Diffusion Financial Market with Common Shock Dependence

作　　者：靳冰岩 马世霞[1] JIN Bingyan;MA Shixia(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《应用数学》2021年第2期342-356,共15页Mathematica Applicata

基　　金：Supported by the Natural Science Foundation of China(11471218,11301133)。

摘　　要：在本文中,我们考虑跳扩散模型下具有延迟和违约风险的鲁棒最优再保险和投资问题,保险人可以投资无风险资产,可违约的债券和两个风险资产,其中两个风险资产遵循跳跃扩散模型且受到同种因素带来共同影响而相互关联.假设允许保险人购买比例再保险,特别地再保险保费利用均值方差保费原则来计算.在考虑与绩效相关的资本流入/流出下,保险公司的财富过程通过随机微分延迟方程建模.保险公司的目标是最大程度地发挥终端财富和平均绩效财富组合的预期指数效用,以分别研究违约前和违约后的情况.此外,推导了最优策略的闭式表达式和相应的价值函数.最后通过数值算例和敏感性分析,表明了各种参数对最优策略的影响.另外对于模糊厌恶投资者,忽视模型模糊性风险会带来显著的效用损失.In this paper,we consider a robust optimal reinsurance and investment problem with delay and default risk under jump-diffusion model.The insurer can trade in a risk-free asset,a defaultable bond and two risky assets whose price processes are described by jump-diffusion models and correlated through a common shock.Assume that the insurer is allowed to purchase proportional reinsurance,in particular,the reinsurance premium is assumed to be calculated via the mean-variance premium principle.Under the consideration of the performance-related capital inflow/outflow,the wealth process of the insurer is modeled by a stochastic differential delay equation.The insurer’s aim is to maximize the expected exponential utility of the combination of terminal wealth and average performance wealth to study the pre-default and post-default case respectively.Furthermore,closed-form expressions for the optimal strategies and the corresponding value function are derived.Finally,numerical examples and sensitivity analyses are provided to show the impact of various parameters on the optimal strategies.In addition,ignoring model uncertainty risk will lead to significant utility loss for the Ambiguity-Averse insurers.

关 键 词：鲁棒最优控制 跳扩散模型 共同冲击相依性 随机微分延迟方程 违约风险 

分 类 号：O211.6[理学—概率论与数理统计] O29[理学—数学]