相依风险模型下具有延迟和违约风险的鲁棒最优投资和再保险策略  

ROBUST OPTIMAL INVESTMENT AND REINSURANCE STRATEGIES WITH DELAY AND DEFAULT RISK UNDER DEPENDENT RISK MODEL

作　　者：慕蕊 马世霞[1] 张欣茹 MU Rui;MA Shi-xia;ZHANG Xin-ru(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：《数学杂志》2022年第4期300-314,共15页Journal of Mathematics

基　　金：Supported by the Natural Science Foundation of China(12071107)。

摘　　要：本文研究了在风险相依模型下具有延迟和违约风险的鲁棒最优投资再保险策略.假设模糊厌恶型保险人的财富过程有两类相依的保险业务并且余额可以投资于无风险资产、可违约债券和价格过程遵循Heston模型的风险资产.利用动态规划原则,我们分别建立了违约后和违约前的鲁棒HJB方程.另外,通过最大化终端财富的期望指数效用,我们得到了最优投资和再保险策略以及相应的值函数.最后,通过一些数值例子说明了某些模型参数对鲁棒最优策略的影响.In this paper,we consider the robust optimal investment-reinsurance strategies with delay and default risk under risk dependent model.We assume that the ambiguity-averse insurer s wealth process have two dependent classes of insurance business and the surplus can invest in a risk-free asset,a defaultable bond and a risky asset whose price process satisfies Heston model.Using dynamic programming principle,we establish the robust Hamilton-Jacobi-Bellman(HJB)equations for the post-default case and the pre-default case,respectively.Furthermore,we obtain the robust optimal investment and reinsurance strategies and the corresponding value functions by maximizing the expected exponential utility of the terminal wealth.Finally,we provide numerical examples to illustrate the effects of some model parameters on the robust optimal strategies.

关 键 词：鲁棒最优策略 Heston模型 随机微分延迟方程 相依风险 违约风险 

分 类 号：O211.6[理学—概率论与数理统计] O29[理学—数学]