华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (1): 70-77.

• 数学 • 上一篇    下一篇

有投资回报的更新风险模型的破产概率的上界(英）

徐林1,2, 汪荣明1,\ 姚定俊1   

  • 收稿日期:2006-04-17 修回日期:2006-09-20 出版日期:2007-01-25 发布日期:2007-01-25
  • 通讯作者: 徐林

Upper Bound for Renewal Risk Model with Stochastic Investment Return(English)

XU Lin1,2, WANG Rong-ming1 , YAO Ding-jun1   

  1. 1. Department of Statistics, East China Normal University, Shanghai 200062, China; 2. School of Mathematics and Computer science, Anhui NormalUniversity, Wuhu Anhui 241000, China
  • Received:2006-04-17 Revised:2006-09-20 Online:2007-01-25 Published:2007-01-25
  • Contact: XU Lin

摘要： 研究了在投资回报过程为指数勒维过程的情形下的更新风险模型的的破产问题. 通过构造一个和破产时刻有关的上鞅, 得到了终极破产概率的鞅上界,并用数值方法考察了理赔间隔的分布对破产概率的影响.

关键词: 更新风险模型, 勒维过程, 破产概率, 鞅方法, 更新风险模型, 勒维过程, 破产概率, 鞅方法

Abstract: Ruin problems in the ordinary renewal risk model with stochastic investment were examined. The asset price process of investment is denoted by $\{e^{R_t},\ t\geqslant 0\}$, where $R_t$ is assumed to be a L\'{e}vy process. By constructing a supermartingale associated with the ruin time of the surplus process with investment, an upper bound for ultimate ruin probability by
martingale approach was presented. The impact of inter-arrival times of claims on ruin probability was considered by numerical method.

Key words: L\'{e}vy process, ruin probability, martingale , ordinary renewal risk model, L\'{e}vy process, ruin probability, martingale

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