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http://dx.doi.org/10.7465/jkdi.2013.24.1.1

Ruin probabilities in a risk process perturbed by diffusion with two types of claims  

Won, Ho Jeong (Department of Statistics, Sookmyung Women's University)
Choi, Seung Kyoung (Department of Statistics, Sookmyung Women's University)
Lee, Eui Yong (Department of Statistics, Sookmyung Women's University)
Publication Information
Journal of the Korean Data and Information Science Society / v.24, no.1, 2013 , pp. 1-12 More about this Journal
Abstract
In this paper, we introduce a continuous-time risk model where the surplus follows a diffusion process with positive drift while being subject to two types of claims. We assume that the sizes of both types of claims are exponentially distributed and that type I claims occur more frequently, however, their sizes are smaller than type II claims. We obtain the ruin probability that the level of the surplus becomes negative, by establishing an integro-differential equation for the ruin probability. We also obtain the 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 to compare the impacts of two types of claim on the ruin probability of the surplus with that of the diffusion process in the risk model.
Keywords
Diffusion process; integro-differential equation; risk model; ruin probability; surplus;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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