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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국통계학회 JKSS(Journal of the Korean Statistical Society) Journal of the Korean Statistical Society 제41권 제3호
- 발행연도
- 2012.1
- 수록면
- 387 - 397 (11page)
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초록· 키워드
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In this paper, we consider an extension to the continuous time risk model for which the occurrence of the claim may be delayed and the time of delay for the claim is assumed to be random. Two types of dependent claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim. The time of occurrence of a by-claim is later than that of its associate main claim and the time of delay for the occurrence of a by-claim is random. An integro-differential equations system for the Gerber-Shiu discounted penalty function is established using the auxiliary risk models. Both the system of Laplace transforms of the Gerber-Shiu discounted penalty functions and the Gerber-Shiu discounted penalty functions with zero initial surplus are obtained. From Lagrange interpolating theorem, we prove that the Gerber-Shiu discounted penalty function satisfies a defective renewal equation. Exact representation for the solution of this equation is derived through an associated compound geometric distribution. Finally, examples are given with claim sizes that have exponential and a mixture of exponential distributions.
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