Lévy模型下的最优寿险、消费和投资  

Optimal Life Insurance,Consumption and Investment Problem in a Lévy Model

作　　者：陈旭 Xu Chen(College of Mathematics and Statistics,Hunan Normal University,Changsha 410081)

机构地区：[1]湖南师范大学数学与统计学院,长沙410081

出　　处：《数学物理学报（A辑）》2022年第1期306-320,共15页Acta Mathematica Scientia

基　　金：湖南省教育厅重点项目(19A294)。

摘　　要：利用最小最大鞅测度方法研究了一个具有不确定寿命的有工资收入者(职员)所面临的最优寿险消费投资问题.金融市场由一种无风险资产和一种风险资产组成,风险资产价格动态由指数Lévy过程刻画.工资所有者的目标是期望效用最大化.基于最小最大鞅测度,该文得到了各种效用函数下最优策略的显式解,并通过数值模拟讨论了参数对最优策略的影响.In this paper,we employ the Minimax martingale measure to investigate an optimal life insurance-consumption-investment problem faced by a wage-eaener with an uncertain lifetime.The financial market is comprised of one risk-free security and a risky security whose price is determined by an exponential Levy process.The object of the wage-eaener is to maximize the expected utility.Based on the Minimax martingale measure,the explicit solutions for various utility functions are obtained.Furthermore,a numerical example is considered,and numerical simulations are presented to illustrate the effect of the parameters on the optimal strategies.

关 键 词：最优寿险消费投资 LÉVY过程 最小最大鞅测度 

分 类 号：O211.9[理学—概率论与数理统计]