考虑Vasicek利率和相依风险的最优投资与再保险  

Optimal Investment and Reinsurance with Vasicek Interest Rate and Dependent Risk

作　　者：米辉[1] 狄文荣 林金官[2] MI Hui;DI Wenrong;LIN Jinguan(School of Mathematical Sciences,Nanjing Normal University,Nanjing,210023,China;School of Statistics and Data Science,Nanjing Audit University,Nanjing,211815,China)

机构地区：[1]南京师范大学数学科学学院,南京210023 [2]南京审计大学统计与数据科学学院,南京211815

出　　处：《应用概率统计》2023年第2期239-258,共20页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11971235、11831008)资助。

摘　　要：本文研究了利率由Vasicek过程描述,两类保险业务具有相依风险的最优投资和再保险模型.盈余过程由扩散近似模型刻画,保险人的目标是在给定期望终端财富的情况下,寻找使得终端财富的方差最小的投资和再保险策略.通过使用随机线性二次最优控制理论,建立Hamilton-Jacobi-Bellman(HJB)方程,我们获得了值函数的精确表达式以及最优投资和再保险策略.另外,我们给出了有效策略和有效前沿.最后,通过数值例子说明了模型参数对最优投资和再保险策略的影响.This paper studies an optimal investment and reinsurance problem in which the interest rate is driven by the Vasicek process,the surplus process is governed by a diffusion approximation model and two dependent classes of insurance business correlated through a common shock component are considered.The objective of the insurer is to minimize the variance of terminal wealth for a given terminal expected wealth.By using the stochastic linear-quadratic(LQ)control theory and the corresponding Hamilton-Jacobi-Bellman(HJB)equation,we obtain the explicit expressions for the value function,and the optimal investment and reinsurance strategies.Furthermore,the efficient strategies and efficient frontier are derived explicitly.Finally,some examples are given to show the influence of model parameters on the optimal investment and reinsurance strategies.

关 键 词：投资–再保险策略 相依风险 均值–方差 HJB方程 Vasicek随机利率 

分 类 号：O211.6[理学—概率论与数理统计] F830[理学—数学]