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有随机投资回报的随机保费模型的渐近破产概率(英文)
引用本文:徐林,汪荣明.有随机投资回报的随机保费模型的渐近破产概率(英文)[J].数学杂志,2010,30(3).
作者姓名:徐林  汪荣明
作者单位:1. 安徽师范大学数学与计算机科学学院,安徽,芜湖,241003
2. 华东师范大学金融与统计学院,上海,200241
基金项目:国家自然科学基金,the Doctoral Program Foundation of the Ministry of Education of China,the National Basic Research Program of China(973 Program),the NSF of Anhui Educational Bureau 
摘    要:本文研究了随机投资回报环境下扰动的随机保费模型的破产问题.利用鞅方法和随机分析的理论讨论了盈余过程的一些基本性质,得到了一个可以用来求解破产时刻的Laplace变换的积分微分方程,结果推广了已有的随机投资问报风险模型的结论.

关 键 词:鞅方法  破产概率  积分微分方程  随机微分方程

ASYMPTOTIC RUIN PROBABILITIES FOR RISK MODEL WITH RANDOM PREMIUM AND STOCHASTIC RETURN ON INVESTMENT
XU Lin,WANG Rong-ming.ASYMPTOTIC RUIN PROBABILITIES FOR RISK MODEL WITH RANDOM PREMIUM AND STOCHASTIC RETURN ON INVESTMENT[J].Journal of Mathematics,2010,30(3).
Authors:XU Lin  WANG Rong-ming
Institution:XU Lin~1,WANG Rong-ming~2 (1.School of Math., Computer Sciences,Anhui Normal University,Wuhu 241003,China) (2.School of Finance , Statistics,East China Normal University,Shanghai 200241,China)
Abstract:In this article,the perturbed classical risk model allows for extra stochastic premium income and stochastic return on investment are studied.By applying martingale method and theory related to stochastic analysis,some properties of risk model are presented and an integro-differential equation for solving the Laplace transform of the ruin time is established.The results of this article generalize some results on the risk model without stochastic premium income.
Keywords:integro-differential equation  stochastic differential equation  martingale method  ruin probability  stochastic premium
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