On the complete monotonicity of the compound geometric convolution with applications in risk theory

Sung Nok Chiu; Chuancun Yin

doi:10.1080/03461238.2011.647061

On the complete monotonicity of the compound geometric convolution with applications in risk theory

Sung Nok Chiu, Chuancun Yin

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

9 Citations (Scopus)

56 Downloads (Pure)

Abstract

We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density.

Original language	English
Pages (from-to)	116-124
Number of pages	9
Journal	Scandinavian Actuarial Journal
Issue number	2
DOIs	https://doi.org/10.1080/03461238.2011.647061
Publication status	Published - 2014

Scopus Subject Areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

User-Defined Keywords

complete monotonicity
compound geometric convolution
Pollaczeck-Khinchine formula
ruin probability
Sparre Andersen model

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10.1080/03461238.2011.647061

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abstract = "We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density.",

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note = "Funding Information: SNC was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Nos. HKBU200807 and HKBU200710) and an FRG grant of the Hong Kong Baptist University; CY was supported by the National Natural Science Foundation of China (No. 10771119) and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20093705110002).",

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N2 - We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density.

AB - We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density.

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KW - Pollaczeck-Khinchine formula

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KW - Sparre Andersen model

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On the complete monotonicity of the compound geometric convolution with applications in risk theory

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