Ornstein-Uhlenbeck过程刻画的股票市场下的最优超额损失再保险和投资  

Optimal Excess-of-Loss Reinsurance and Investment in a Stock Market with Ornstein-Uhlenbeck Process

作　　者：黄玲[1] 刘海燕[1] 陈密[1,2,3] HUANG Ling;LIU Haiyan;CHEN Mi(School of Mathematics and Statistics,Fujian Normal University,Fuzhou,350117,China;Key Laboratory of A nalytical Mathematics and Applications(Ministry of Education),Fuzhou,China;Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence,Fuzhou,350117,China)

机构地区：[1]福建师范大学数学与统计学院,福州350117 [2]分析数学及应用教育部重点实验室,福州350117 [3]统计学与人工智能福建省高校重点实验室,福州350117

出　　处：《应用概率统计》2024年第5期741-756,共16页Chinese Journal of Applied Probability and Statistics

基　　金：福建省自然科学基金项目(批准号:2023J01537,2023J01538)资助。

摘　　要：本文在扩散逼近风险模型下研究了保险公司的最优投资和再保险策略.假设保险公司可购买超额损失再保险,并将盈余投资于无风险资产和风险资产组成的金融市场,其中风险资产价格模型受Ornstein-Uhlenbeck过程影响.保险公司的目标是使终端财富的期望指数效用最大化.利用随机控制理论和HJB方程,推导出了最优策略和值函数的显式表达式.最后,通过数值分析讨论了模型参数对最优策略和值函数的影响.This paper studies the optimal investment and excess-of-loss reinsurance strategies in a dif-fusion approximation risk model.It is assumed that the insurance company can purchase excess-of-loss reinsurance and invest its reserve in a financial market composed of a risk-free asset and a risky asset.The price model of risky asset is influenced by an Ornstein-Uhlenbeck process.The goal of the insurance company is to maximize the expected exponential utility of the terminal wealth.Using stochastic control theory and HJB equation,the explicit expressions for optimal strategies and value function are derived.Finally,the influence of model parameters on the optimal strategy and value function is analyzed through numerical analysis.

关 键 词：HJB方程 ORNSTEIN-UHLENBECK过程 指数效用 超额损失再保险 投资 

分 类 号：O211.6[理学—概率论与数理统计]