Ruin Probability in a Compound Poisson Risk Model with a Two-Step Premium Rule

Title & Authors
Ruin Probability in a Compound Poisson Risk Model with a Two-Step Premium Rule
Song, Mi-Jung; Lee, Ji-Yeon;

Abstract
We consider a compound Poisson risk model in which the premiums may depend on the state of the surplus process. By using the overflow probability of the workload process in the corresponding M/G/1 queueing model, we obtain the probability that the ruin occurs before the surplus reaches a given large value in the risk model. We also examplify the ruin probability in case of exponential claims.
Keywords
Ruin probability;compound Poisson risk model;two-step premium rule;M/G/1 queueing model;overflow probability;
Language
Korean
Cited by
1.
A Compound Poisson Risk Model with a Two-Step Premium Rule,;;

Communications for Statistical Applications and Methods, 2013. vol.20. 5, pp.377-385
1.
A Compound Poisson Risk Model with a Two-Step Premium Rule, Communications for Statistical Applications and Methods, 2013, 20, 5, 377
References
1.
이용주(2003). 대재해 위험을 고려한 보험자의 파산확률모형, <경영논총>, 21, 103-124.

2.
이혜선, 최승경, 이의용 (2009). 보험 상품 파산 확률 근사 방법의 개선 연구, <응용통계연구>, 22, 937-942.

3.
이호우(2006). <대기행렬이론: 확률과정론적분석>, 3판, 시그마프레스, 서울

4.
한수희, 이의용 (2006). 브라운 운동을 이용한 보험 상품의 파산 모형 연구, <응용통계연구>, 19, 579-585.

5.
Asmussen, S. (2003). Applied Probability and Queues, 2nd ed., Springer, New York.

6.
Asmussen, S. and Petersen, S. S. (1988). Ruin probabilities expressed in terms of storage processes, Advances in Applied Probability, 20, 913-916.

7.
Bae, J., Kim, S. and Lee, E. Y. (2002). A $P_{M}^{\lambda}-policy$ for an M/G/1 queueing system, Applied Mathematical Modeling, 26, 929-939.

8.
Gerber, H. U. (1990). When does the surplus reach a given target?, Insurance: Mathematics and Economics, 9, 115-119.

9.
Gerber, H. U. and Shiu, E. S. W. (1998). On the time value of ruin, North American Actuarial Journal, 2, 48-78.

10.
Lee, J. (2007). First exit times for compound Poisson dams with a general release rule, Mathematical Methods for Operations Research, 65, 169-178.

11.
Lin, X. S. and Pavlova, K. P. (2006). The compound Poisson risk model with a threshold dividend strategy, Insurance: Mathematics and Economics, 38, 57-80.

12.
Lin, X. S. and Willmot, G. E. (1999). Analysis of a defective renewal equation arising in ruin theory, Insurance: Mathematics and Economics, 25, 63-84.

13.
Lin, X. S.,Willmot, G. E. and Drekic, S. (2003). The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function, Insurance: Mathematics and Economics, 33, 551-566.

14.
Oh, S. M., Jeong, M. and Lee, E. Y. (2007). A martingale approach to a ruin model with surplus following a compound Poisson process, Journal of the Korean Statistical Society, 36, 229-235.

15.
Park, H. S. (2010). Computing the ruin probability of Levy insurance risk processes in non-Cramer models, Communications of the Korean Statistical Society, 17, 483-491.

16.
Song, M. J. and Lee, J. (2010). A compound Poisson risk model with a two-step premium rule (submitted).