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Computing Ruin Probability Using the GPH Distribution
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 Title & Authors
Computing Ruin Probability Using the GPH Distribution
Yoon, Bok Sik;
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Even though ruin probability is a fundamental value to determine the insurance premium and policy, the complexity involved in computing its exact value forced us resort to an approximate method. In this paper, we first present an exact method to compute ruin probability under the assumption that the claim size has a GPH distribution, Then, for the arbitrary claim size distribution, we provide a method computing ruin probability quite accurately by approximating the distribution as a GPH. The validity of the proposed method demonstrated by a numerical example. The GPH approach seems to be valid for heavy-tailed claims as well as usual light-tailed claims.
Ruin Probability;Insurance;GPH Distribution;Pollaczeck-Kinchine Formula;
 Cited by
윤복식, 박광우, 이창훈, "GPH 분포에 의한 확률적 근사화", 한국경영과학회지, 제19권, 제1호(1994), pp.85-98.

윤복식, "일반적인 큐잉네트워크에서의 체류시간분포의 근사화", 한국경영과학회지, 제19권, 제3호(1994), pp.93-109.

Asmussen, S. and H. Albrecher, Ruin Probability(2ed.), World Scientific, Singapore, 2010.

Avram, F. and M. Pistorius, "On matrix exponential approximations of ruin probability for the classic and Brownian perturbed Cramer-Lundberg processes," Insurance:Mathematics and Economics, Vol.59(2014), pp.57-64. crossref(new window)

Brekelmans, R. and A. De Waegenaere, Approximating the finite-time ruin probability under interest force, Insurance:Mathematics and Economics, Vol.29(2001), pp.217-229. crossref(new window)

Coulibaly, I. and C. Lefevre, "On a simple quasi-Monte Carlo approach for classical ultimate ruin probabilities," Insurance:Mathematics and Economics, Vol.42(2008), pp.935-942. crossref(new window)

Chen, Y. and K.W. Ng, "The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims," Insurance:Mathematics and Economics, Vol.40(2007), pp.415-423. crossref(new window)

Dickson, D.C.M. and H.R. Waters, "Reinsurance and ruin," Insurance:Mathematics and Economics, Vol.19(1994), pp.61-80.

Grandell, J., "Simple approximations of ruin probabilities," Insurance:Mathematics and Economics, Vol.26(2000), pp.157-173, crossref(new window)

Ignatov, Z.G., V.K. Kaishev, and R.S. Krachunov, "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance:Mathematics and Economics, Vol.29(2001), pp.375-386. crossref(new window)

Kalashnikov, V. and D. Konstantinides, "Ruin under interest force and subexponential claims :a simple treatment," Insurance:Mathematics and Economics, Vol.27(2000), pp.145-149. crossref(new window)

Kalashnikov, V. and R. Norberg, "Power tailed ruin probabilities in the presence of risky investments," Stochastic Processes and their Applications, Vol.98(2002), pp.211-228. crossref(new window)

Shaked, M. and J.G. Shanthikumar, "Phase Type Distributions," in Encyclopedia of Statistical Sciences, 6, John Wiley and Sons, New York(editors S. Kotz and N.L. Johnson), (1985), pp.709-715.

Shanthikumar, J.G., "Bilateral Phase-Type Distributions," Naval Research Logistics Quarterly, Vol.32(1985), pp.119-136. crossref(new window)

Willmot, G.E., "On a class of approximations for ruin and waiting time probabilities," Operations Resaerch Letters, Vol.22(1998), pp.27-32. crossref(new window)