数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 919-931.doi: 10.1016/S0252-9602(10)60089-6

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CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

王姗姗, 张春生, 吴荣   

  1. School of Mathematical Sciences and LPMC, Nankai |University, Tianjin 300071, China
  • 收稿日期:2007-12-10 修回日期:2008-09-17 出版日期:2010-05-20 发布日期:2010-05-20
  • 基金资助:

    This work was supported by National Basic Research Program of China (973 Program, 2007CB814905) and the Natural Science
    Foundation of China (10871102)

CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

 WANG Shan-Shan, ZHANG Chun-Sheng, WU Rong   

  1. School of Mathematical Sciences and LPMC, Nankai |University, Tianjin 300071, China
  • Received:2007-12-10 Revised:2008-09-17 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This work was supported by National Basic Research Program of China (973 Program, 2007CB814905) and the Natural Science
    Foundation of China (10871102)

摘要:

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.

关键词: Probability of ruin, the perturbed classical surplus model, Oscillation, recursive calculation

Abstract:

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.

Key words: Probability of ruin, the perturbed classical surplus model, Oscillation, recursive calculation

中图分类号: 

  • 60J25