Journal article

Analytical expressions of risk quantities for composite models

Jose Maria Sarabia, Enrique Calderin-Ojeda

JOURNAL OF RISK MODEL VALIDATION | INCISIVE MEDIA | Published : 2018

Abstract

Composite models have received a lot of attention in the recent actuarial literature. In this paper, we obtain analytic expressions of different actuarial and statistical quantities for a general class of composite models derived from the McDonald's family of probability distributions. These quantities include probability density functions, cumulative distribution functions, quantile functions, raw moments, value-at-risk, tail moments, moments of loss variables and the quantile density function, which is very useful for the computation of expectations of order statistics. Finally, applications of these models to two sets of unimodal and positively skewed insurance claim size data are provide..

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University of Melbourne Researchers

Grants

Awarded by Programa Estatal de Fomento de la Investigacion Cientifica y Tecnica de Excelencia/Spanish Ministry of Economy and Competitiveness


Awarded by Santander Financial Institute (SANFI) of the UCEIF Foundation


Awarded by Ministerio de Economia y Competitividad, Spain


Funding Acknowledgements

The authors are grateful for the reviewer's helpful suggestions. Also, the first author gratefully acknowledges financial support from the Programa Estatal de Fomento de la Investigacion Cientifica y Tecnica de Excelencia/Spanish Ministry of Economy and Competitiveness, Project ECO2016-76203-C2-1-P. In addition, this work is part of the Research Project APIE 1/2015-17, "New methods for the empirical analysis of financial markets", of the Santander Financial Institute (SANFI) of the UCEIF Foundation, resolved by the University of Cantabria and funded by Banco Santander. The second author thanks Ministerio de Economia y Competitividad, Spain Project ECO2013/47092.