CEV模型和违约风险下具有稀疏相依风险的鲁棒最优再保险和投资策略  

Robust Optimal Investment and Reinsurance Strategies with Thinning Dependent Risks under CEV Model and Default Risk

作　　者：张雨萌 马世霞[1] 张欣茹 

机构地区：[1]河北工业大学理学院,天津

出　　处：《应用数学进展》2023年第3期1022-1034,共13页Advances in Applied Mathematics

摘　　要：本文研究了一个具有稀疏相依风险的模糊厌恶保险公司(AAI)的最优再保险和投资问题。AAI通过购买比例再保险来控制保险风险,再保险保费遵循广义期望值–方差原则,并将其财富投资于一个储蓄账户、股票和可违约债券组成的金融市场,其中股票价格过程服从常方差弹性(CEV)模型。以终端财富的期望指数效用最大为目标,利用随机控制方法分别建立了违约后和违约前的鲁棒Hamilton-Jacobi-Bellman (HJB)方程,并分别推导出鲁棒最优再保险和投资策略和相应的值函数。最后,用数值例子分析了模型参数对鲁棒最优策略的影响并给出相应的经济解释。This paper investigates the optimal reinsurance and investment problem with thinning dependent risks for an ambiguity-averse insurer (AAI). It is assumed that AAI manages insurance risk by pur-chasing proportional reinsurance, in which the reinsurance premium is calculated by the general-ized mean-variance premium principle, and its wealth is invested in a financial market consisting of a saving account, a defaultable bond and a stock whose price process obeys the constant elasticity of variance (CEV) model. The AAI aims to maximize the expected exponential utility of terminal wealth. The HJB equation corresponding to the robust optimal problem is established by using stochastic control method, and the robust optimal strategy and value function are obtained for the pre-default and post-default case respectively. Finally, numerical examples are presented to illustrate the ef-fects of parameters on the robust optimal strategies and the corresponding economic explanations are given.

关 键 词：鲁棒最优控制 稀疏相依 CEV模型 违约风险 

分 类 号：F83[经济管理—金融学]