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ON SUMS OF INDEPENDENT GENERALIZED PARETO RANDOM VARIABLES WITH APPLICATIONS TO INSURANCE AND CAT BONDS

Published online by Cambridge University Press:  04 April 2017

Saralees Nadarajah ,
Yuanyuan Zhang  and
Tibor K. Pogány
Saralees Nadarajah
Affiliation:
School of Mathematics, University of Manchester, Manchester, UK E-mail: mbbsssn2@manchester.ac.uk
Yuanyuan Zhang
Affiliation:
School of Mathematics, University of Manchester, Manchester, UK
Tibor K. Pogány
Affiliation:
Faculty of Maritime Studies, University of Rijeka, Rijeka, CROATIA
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Abstract

We derive single integral representations for the exact distribution of the sum of independent generalized Pareto random variables. The integrands involve the incomplete and complementary incomplete gamma functions. Applications to insurance and catastrophe bonds are described.

Keywords

characteristic functiongeneralized Pareto distributionincomplete gamma function
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 2 , April 2018 , pp. 296 - 305
Copyright
Copyright © Cambridge University Press 2017 

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