Department of Mathematics
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.
complete monotonicity, compound geometric convolution, Pollaczeck-Khinchine formula, ruin probability, Sparre Andersen model
Source Publication Title
Scandinavian Actuarial Journal
Taylor & Francis
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.
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).
Link to Publisher's Edition
Chiu, S., & Yin, C. (2013). On the complete monotonicity of the compound geometric convolution with applications in risk theory. Scandinavian Actuarial Journal, 2, 116-124. https://doi.org/10.1080/03461238.2011.647061