The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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The Ruin Probability in a Risk Model with Injections

재충전이 있는 연속시간 리스크 모형에서 파산확률 연구

  • Go, Han-Na (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)
  • 고한나 (숙명여자대학교 통계학과) ;
  • 최승경 (숙명여자대학교 통계학과) ;
  • 이의용 (숙명여자대학교 통계학과)
  • Received : 2011.09.30
  • Accepted : 2011.12.26
  • Published : 2012.02.29
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Abstract

A continuous time risk model is considered, where the premium rate is constant and the claims form a compound Poisson process. We assume that an injection is made, which is an immediate increase of the surplus up to level u > 0 (initial level), when the level of the surplus goes below ${\tau}$(0 < ${\tau}$ < u). We derive the formula of the ruin probability of the surplus by establishing an integro-differential equation and show that an explicit formula for the ruin probability can be obtained when the amounts of claims independently follow an exponential distribution.

재충전이 있는 연속시간 리스크 모형이 고려된다. 프레미엄은 일정한 율로 들어오고, 보험금 청구는 복합 포아송 과정을 따라 이루어진다. 초기 잉여금 u > 0로 시작하여 잉여금은 프레미엄에 의해 증가하고 보험금 청구에 의해 감소한다. 잉여금의 수준이 ${\tau}$(0 < ${\tau}$ < u)아래로 떨어지면 초기 잉여금 수준까지 재충전이 이루어진다고 가정한다. 재충전이 고려된 리스크 모형에서 잉여금이 없어지는 파산확률을 적미분 방정식을 통해 유도하고, 보험 청구액이 독립적으로 지수분포를 따르는 경우는 파산확률의 명확한 공식이 유도됨을 보인다.

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References

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