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Surplus Process Perturbed by Diffusion and Subject to Two Types of Claim

  • Choi, Seung Kyoung (Department of Statistics, Sookmyung Women's University) ;
  • Won, Hojeong (Department of Statistics, Sookmyung Women's University) ;
  • Lee, Eui Yong (Department of Statistics, Sookmyung Women's University)
  • Received : 2014.12.19
  • Accepted : 2015.01.07
  • Published : 2015.01.31

Abstract

We introduce a surplus process which follows a diffusion process with positive drift and is subject to two types of claim. We assume that type I claim occurs more frequently, however, its size is stochastically smaller than type II claim. We obtain the ruin probability that the level of the surplus becomes negative, and then, decompose the ruin probability into three parts, two ruin probabilities caused by each type of claim and the probability that the level of the surplus becomes negative naturally due to the diffusion process. Finally, we illustrate a numerical example, when the sizes of both types of claim are exponentially distributed, to compare the impacts of two types of claim on the ruin probability of the surplus along with that of the diffusion process.

Acknowledgement

Supported by : Sookmyung Women's University

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