双复合泊松风险模型下的投资问题  

A Proportional Investment Problem under the Double Compound Poisson Risk Model

作　　者：袁野 邓飞其 

机构地区：[1]华南理工大学数学学院,广东广州510640

出　　处：《经济数学》2018年第1期16-22,共7页Journal of Quantitative Economics

基　　金：国家自然科学基金资助项目(61573156)

摘　　要：在经典风险模型基础上,研究了保险公司保费收入和索赔均服从复合泊松过程的双复合泊松风险模型,针对最优投资策略和求解破产时刻惩罚金期望折现函数的问题,利用重期望公式和马氏性得到期望折现函数满足的带边界条件的二阶积分微分方程,通过高效的Sinc数值方法求出折现函数的近似数值解,从而由图像分析破产概率变化的趋势.Based on the classical risk model,we studied the double compound Poisson risk model in which the insurance company＇s premium follows a compound Poisson process and the claims also follow a compound Poisson process. Consider the optinal investment and the expected discount penalty function,by using the heavy expectation formula and Markov property, we obtained the second order integro-differential equation with boundary conditions, a numerical Sinc method was proposed to derive a approximate numerical solution, then we can analyze the ruin probability by the figure of approximate numerical solution.

关 键 词：双复合泊松过程 重期望公式 马氏性 积分微分方程 Sinc数值方法 

分 类 号：O211.6[理学—概率论与数理统计]