在跳跃扩散模型下带延迟和错误定价的超额损失再保险和投资的最优化问题  

OPTIMIZATION PROBLEM OF EXCESS-OF-LOSS REINSURANCE AND INVESTMENT WITH DELAY AND MISPRICING UNDER THE JUMP-DIFFUSION MODEL

作　　者：黄晴 马世霞[1] 龚晓琴 HUANG Qing;MA Shi-xia;GONG Xiao-qin(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《数学杂志》2020年第2期185-198,共14页Journal of Mathematics

基　　金：Supported by the Natural Science Foundation of China(11471218,11301133).

摘　　要：本文研究了在跳跃扩散模型下带延迟和错误定价的超额损失再保险和投资的最优化问题.利用随机控制理论,求解扩展的HJB方程,推导出均衡再保险投资策略和相应的均衡值函数.最后,介绍模型和结果的一些特殊情况,并为其结果提供了一些数值分析.In this paper,we study an optimization problem of excess-of-loss reinsurance and investment with delay and mispricing under the Jump-diffusion model.Using the stochastic control theory,the equilibrium reinsurance-investment strategy and the corresponding equilibrium value function are derived by solving an extended HJB system.Finally,some special cases of our model and results are presented,and some numerical examples for our results are provided.

关 键 词：超额损失再保险 Levy保险模型 错误定价 随机微分延迟方程 跳跃-扩散模型 

分 类 号：F840[经济管理—保险]