Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Ruin Probability in a Compound Poisson Risk Model with a Two-Step Premium Rule

이단계 보험요율의 복합 포아송 위험 모형의 파산 확률

  • Song, Mi-Jung (Department of Statistics, Yeungnam University) ;
  • Lee, Ji-Yeon (Department of Statistics, Yeungnam University)
  • Received : 20110200
  • Accepted : 20110600
  • Published : 2011.07.31
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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.

잉여금의 수준에 따라 이단계의 보험요율이 적용되는 복합 포아송 위험 모형을 고려한다. 먼저 이 위험 모형에 대응되는 이단계 서비스율의 M/G/1 대기행렬 모형을 설정하고, M/G/1 대기행렬 모형에서 작업량이 0에 도달하기 전에 과부하가 발생하는 확률을 유도한다. 이과부하 확률을 이용하여 위험모형에서 잉여금이 목표값에 도달하기 전에 파산하는 확률을 구하고, 보험 청구액이 지수분포를 따르는 경우의 파산 확률을 계산한다.

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