Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments

41 Pages Posted: 29 Feb 2016

See all articles by Gareth Peters

Gareth Peters

University of California Santa Barbara; affiliation not provided to SSRN

Wilson Chen

University of Sydney Business School

Richard H. Gerlach

University of Sydney

Date Written: February 28, 2016

Abstract

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterizations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling.

One of the challenges with such models is to perform robust estimation for the loss model parameters that will be amenable to practitioners when fitting such models. In this paper we develop a novel, efficient and robust estimation procedure for estimation of model parameters in this family Tukey transform models, based on L-moments. It is shown to be more robust and efficient than current state of the art methods of estimation for such families of loss models and is simple to implement for practical purposes.

Keywords: Non-life Insurance, Claims Modelling, Quantile Models, g-and-h, g-and-k, g-and-j, loss modelling

JEL Classification: C13, G22

Suggested Citation

Peters, Gareth and Chen, Wilson and Gerlach, Richard H., Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments (February 28, 2016). Available at SSRN: https://ssrn.com/abstract=2739417 or http://dx.doi.org/10.2139/ssrn.2739417

Gareth Peters (Contact Author)

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

affiliation not provided to SSRN

Wilson Chen

University of Sydney Business School

Cnr. of Codrington and Rose Streets
Sydney, NSW 2006
Australia

Richard H. Gerlach

University of Sydney ( email )

Room 483, Building H04
University of Sydney
Sydney, NSW 2006
Australia
+ 612 9351 3944 (Phone)
+ 612 9351 6409 (Fax)

HOME PAGE: http://www.econ.usyd.edu.au/staff/richardg

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