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http://dx.doi.org/10.5351/KJAS.2009.22.5.937

An Improvement of the Approximation of the Ruin Probability in a Risk Process  

Lee, Hye-Sun (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
The Korean Journal of Applied Statistics / v.22, no.5, 2009 , pp. 937-942 More about this Journal
Abstract
In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder's and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.
Keywords
Surplus process; Poisson process; risk model; run probability; approximation formula;
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  • Reference
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