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New approximation method for ruin probabilities using the mixture of exponential distributions
Journal of the Korean Data & Information Science Society 2018;29:189-202
Published online January 31, 2018
© 2018 Korean Data and Information Science Society.

Daehyeon Jung1 · Jiyeon Lee2

12Department of Statistics, Yeungnam University
Correspondence to: Professor, Department of Statistics, Yeungnam University, Kyeongsan 38541, Korea. E-mail: leejy@yu.ac.kr
Received November 27, 2017; Revised January 3, 2018; Accepted January 8, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The ruin probability, one of the important criteria for determining the risk of an insurance product is defined as the probability that the continuous-time surplus process falls below zero. Generally, it is very complicated to calculate the exact ruin probability which depends on the arrival process of the claims and the distribution of the insurance claim amount. Therefore, much efforts have been made to get the approximate value instead of the exact value for the ruin probability. In this paper, we propose a new method to approximate the ruin probability by fitting the first four moments of the loss process with claims which are distributed by the mixture of two exponentials and we compare it with the other approximation methods.
Keywords : Adjustment coefficient, approximation, loss process, ruin probability, surplus process.