The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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An optimal management policy for the surplus process with investments

재투자가 있는 잉여금 과정의 최적 운용정책

  • Lim, Se-Jin (Department of Statistics, Sookmyung Women's University) ;
  • Choi, Seungkyoung (Department of Statistics, Sookmyung Women's University) ;
  • Lee, Eui-Yong (Department of Statistics, Sookmyung Women's University)
  • 임세진 (숙명여자대학교 통계학과) ;
  • 최승경 (숙명여자대학교 통계학과) ;
  • 이의용 (숙명여자대학교 통계학과)
  • Received : 2016.04.27
  • Accepted : 2016.07.19
  • Published : 2016.12.31
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Abstract

In this paper, a surplus process with investments is introduced. Whenever the level of the surplus reaches a target value V > 0, amount S($0{\leq}S{\leq}V$) is invested into other business. After assigning three costs to the surplus process, a reward per unit amount of the investment, a penalty of the surplus being empty and the keeping (opportunity) cost per unit amount of the surplus per unit time, we obtain the long-run average cost per unit time to manage the surplus. We prove that there exists a unique value of S minimizing the long-run average cost per unit time for a given value of V, and also that there exists a unique value of V minimizing the long-run average cost per unit time for a given value of S. These two facts show that an optimal investment policy of the surplus exists when we manage the surplus in the long-run.

보험 상품의 잉여금은 보험료 수입에 의해 증가하며 고객이 보험료를 청구할 때 감소한다. 보험회사는 잉여금이 충분히 많아지면 잉여금의 일부를 재투자하는 것을 통해 이익을 창출한다. 본 연구에서는 보험료 수입과 청구를 고려하여 잉여금의 수준을 나타낸 기존의 잉여금 모형을 소개하고 기존의 모형에 재투자의 개념과 운용비용을 도입하여 장시간에 걸친 단위시간당 평균비용을 구하고, 이를 최소화하는 재투자 수준과 목표 잉여금을 구한다.

Keywords

References

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