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一类包含可违约资产和由Ornstein-Uhlenbeck过程刻画的股票的最优再保险和投资问题(英文)
引用本文:马建静,王过京.一类包含可违约资产和由Ornstein-Uhlenbeck过程刻画的股票的最优再保险和投资问题(英文)[J].应用概率统计,2019(2):111-125.
作者姓名:马建静  王过京
作者单位:苏州大学金融工程研究中心;山东工商学院数学与信息科学学院
基金项目:supported by the National Natural Science Foundation of China(Grant Nos.11771320,11871050);the Shandong Natural Science Foundation(Grant No.ZR2013AM011)
摘    要:本文中,保险人被许可投资于三种金融资产:一个可违约公司零息债券,一个无违约风险的储蓄账户和一个股票.其中,股票的即时回报率由Ornstein-Uhlenbeck过程来刻画.保险人的目标是最大化终值财富的指数期望效用.我们将此优化问题分解为违约前和违约后两个问题,通过动态规划原理,然后求解对应的HJB方程,得到了最优策略和最优值函数的显式解.

关 键 词:可违约资产  再保险与投资  ORNSTEIN-UHLENBECK过程  HAMILTON-JACOBI-BELLMAN方程

An Optimal Reinsurance and Investment Problem with a Defaultable Security and a Stock with Ornstein-Uhlenbeck Process
Institution:(Center for Financial Engineering, Soochow University, Suzhou, 215006, China;chool of Mathematics and Information Science, Shandong Technology and Business University, Yantai, 264005, China)
Abstract:In this paper, the insurer is allowed to buy reinsurance and allocate his money among three financial securities: a defaultable corporate zero-coupon bond, a default-free bank account, and a stock, while the instantaneous rate of the stock is described by an Ornstein-Uhlenbeck process. The objective is to maximize the exponential utility of the terminal wealth. We decompose the original optimization problem into two subproblems: a pre-default case and a post-default case. Using dynamic programming principle, and then solving the corresponding HJB equations,we derive the closed-form solutions for the optimal reinsurance and investment strategies and the corresponding value functions.
Keywords:defaultable security  reinsurance and investment  Ornstein-Uhlenbeck process  Hamilton-Jacobi-Bellman equation
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