基于索赔相依的时滞均衡投资与再保险策略  

Equilibrium Investment and Reinsurance Strategy with Delay and Correlated Claims

作　　者：阎方 刘伟[1] 刘国欣[2] YAN Fang;LIU Wei;LIU Guoxin(College of Mathematics and System Science,Xinjiang University,Urumqi 830046,China;School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046 [2]河北工业大学理学院,天津300401

出　　处：《应用数学》2023年第2期550-561,共12页Mathematica Applicata

基　　金：国家自然科学基金(11961064);国家自然科学基金(12071107)。

摘　　要：本文研究保险公司的最优投资与再保险问题.假设再保险种类是比例再保险,未来索赔与历史索赔是相关的.此外,风险资产的价格过程由常方差弹性模型来描述,并且在财富过程中考虑了财富的时滞效应.在均值-方差优化准则下,本文给出了最优均衡投资和比例再保险策略及值函数的显式解.最后,通过数值分析,讨论了模型主要参数对最优策略的影响.本文所提模型及所获结果是对文献中已有研究成果的推广.This paper studies the optimal investment-reinsurance problem of insurers.Assuming that the type of reinsurance is proportional reinsurance,future claims are related to historical claims.In addition,the price process of risky asset is described by the constant variance elasticity model,and the time delay effect of wealth is considered in the wealth process.In this paper,explicit solutions of optimal equilibrium investment and proportional reinsurance strategies and value functions are given under the mean-variance optimization criterion.Finally,the influence of the main parameters of the model on the optimal strategy is discussed by numerical analysis.The model proposed in this paper and the results obtained are the extension of the existing research results in the literature.

关 键 词：索赔相依 时滞 均值-方差 投资与再保险 HJB方程 

分 类 号：F840[经济管理—保险] O211[理学—概率论与数理统计]