The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Further study on the risk model with a continuous type investment

연속적으로 투자가 이루어지는 보험상품 리스크 모형의 추가 연구

  • 최승경 (숙명여자대학교 통계학과) ;
  • 이의용 (숙명여자대학교 통계학과)
  • Received : 2018.09.06
  • Accepted : 2018.10.10
  • Published : 2018.12.31
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Abstract

Cho et al. (Communications for Statistical Applications and Methods, 23, 423-432, 2016) introduced a risk model with a continuous type investment and studied the stationary distribution of the surplus process. In this paper, we extend the earlier analysis by assuming that additional instant investment is made when the surplus process reaches a certain sufficient level. We obtain the explicit form of the stationary distribution of the surplus process. The case is shown as an example, when the amount of claim is exponentially distributed.

Cho 등 (Communications for Statistical Applications and Methods, 23, 423-432, 2016)은 잉여금이 적정수준에 이르면 연속적으로 투자가 이루어지는 보험상품 리스크 모형을 소개하고, 잉여금 과정의 정상분포함수를 연구하였다. 본 논문에서는 잉여금이 적정수준을 넘어 또 다른 충분한 수준에 이르게 되면 추가로 즉시 투자가 이루어진다고 가정하고 기존의 연구를 확장한다. 잉여금 과정의 정상분포함수를 명확히 구하고, 보험청구액의 분포가 지수분포인 경우를 예제로 다룬다.

Keywords

GCGHDE_2018_v31n6_751_f0001.png 이미지

Figure 1.1. A sample path of {U(t), t ≥ 0}.

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