Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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.

Keywords

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

Publication Date

11-30-2013

Source Publication Title

Scandinavian Actuarial Journal

Volume

2

Start Page

116

End Page

124

Publisher

Taylor & Francis

Peer Reviewed

1

Copyright

This is an Accepted Manuscript of an article published by Taylor & Francis in Scandinavian Actuarial Journal in March 2014, available online: http://dx.doi.org/10.1080/03461238.2011.647061.

Funder

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).

DOI

10.1080/03461238.2011.647061

ISSN (print)

03461238

ISSN (electronic)

16512030

Included in

Mathematics Commons

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