Mean-variance problem for an insurer with default risk under a jump-diffusion risk model
Mean-variance problem for an insurer with default risk under a jump-diffusion risk model
复制标题
跳跃扩散风险模型下具有违约风险的保险公司的均值-方差问题
DOI：
10.1080/03610926.2018.1490432
复制
发表时间：
2019
影响因子：
0.8
通讯作者：
Zhao Hui
中科院分区：
文献类型：
--
作者：
Wang Suxin;Rong Ximin;Zhao Hui
摘要 本文考虑均值-方差准则下具有违约风险的最优投资再保险问题。我们假设保险公司被允许购买比例再保险并将其盈余投资于无风险资产、股票和可违约债券。目标是最大化终端财富的期望并最小化终端财富的方差。我们首先将问题表述为带有约束的随机线性二次（LQ）控制问题。然后分别通过违约后和违约前情况下的 Hamilton-Jacobi-Bellman (HJB) 方程的粘度解获得最优投资再保险策略和相应的价值函数。最后，我们提供数值例子来说明模型参数对最优策略和价值函数的影响。
Abstract This paper considers an optimal investment-reinsurance problem with default risk under the mean-variance criterion. We assume that the insurer is allowed to purchase proportional reinsurance and invest his/her surplus in a risk-free asset, a stock and a defaultable bond. The goal is to maximize the expectation and minimize the variance of the terminal wealth. We first formulate the problem to stochastic linear-quadratic (LQ) control problem with constraints. Then the optimal investment-reinsurance strategies and the corresponding value functions are obtained via the viscosity solutions of Hamilton-Jacobi-Bellman (HJB) equations for the post-default case and pre-default case, respectively. Finally, we provide numerical examples to illustrate the effects of model parameters on the optimal strategies and value functions.