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Beta transform and discounted aggregate claims under dependency

Published online by Cambridge University Press:  13 July 2018

Zhehao Zhang  and
Shuanming Li
Zhehao Zhang*
Affiliation:
Department of Economics, Centre for Actuarial Studies, The University of Melbourne, Parkville, VIC 3010, Australia
Shuanming Li
Affiliation:
Department of Economics, Centre for Actuarial Studies, The University of Melbourne, Parkville, VIC 3010, Australia
*
*Correspondence to: Zhehao Zhang, Department of Economics, Centre for Actuarial Studies, The University of Melbourne, Parkville, VIC 3010, Australia. Tel: +61 3 83445616. E-mail: zhehaoz1@student.unimelb.edu.au
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Abstract

This paper starts with the Beta transform and discusses the stochastic ordering properties of this transform under different parameter settings. Later, the distribution of discounted aggregate claims in a compound renewal risk model with dependence between inter-claim times and claim sizes is studied. Recursive formulas for moments and joint moments are expressed in terms of the Beta transform of the inter-claim times and claim severities. Particularly, our moments formula is more explicit and computation-friendly than earlier ones in the references. Lastly, numerical examples are provided to illustrate our results.

Keywords

Discounted aggregate claimsRenewal risk processCopulaBeta distributional transformStochastic ordering
Type
Paper
Information
Annals of Actuarial Science , Volume 13 , Issue 2 , September 2019 , pp. 241 - 267
Copyright
© Institute and Faculty of Actuaries 2018 

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