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Comparing the riskiness of dependent portfolios via nested L-statistics

Published online by Cambridge University Press:  08 November 2016

Ranadeera G.M. Samanthi ,
Wei Wei  and
Vytaras Brazauskas
Ranadeera G.M. Samanthi
Affiliation:
Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859, USA
Wei Wei
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA
Vytaras Brazauskas*
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA
*
*Correspondence to: Vytaras Brazauskas, Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA. Tel: 1-414-229-5656; Fax: 1-414-229-4907; E-mail: vytaras@uwm.edu
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Abstract

A non-parametric test based on nested L-statistics and designed to compare the riskiness of portfolios was introduced by Brazauskas et al. (2007). Its asymptotic and small-sample properties were primarily explored for independent portfolios, though independence is not a required condition for the test to work. In this paper, we investigate how performance of the test changes when insurance portfolios are dependent. To achieve that goal, we perform a simulation study where we consider three different risk measures: conditional tail expectation, proportional hazards transform, and mean. Further, three portfolios are generated from exponential, Pareto, and lognormal distributions, and their interdependence is modelled with the three-dimensional t and Gaussian copulas. It is found that the presence of strong positive dependence (comonotonicity) makes the test very liberal for all the risk measures under consideration. For types of dependence that are more common in an insurance environment, the effect of dependence is less dramatic but the results are mixed, i.e., they depend on the chosen risk measure, sample size, and even on the test’s significance level. Finally, we illustrate how to incorporate such findings into sensitivity analysis of the decisions. The risks we analyse represent tornado damages in different regions of the United States from 1890 to 1999.

Keywords

CopulasDependent risksRisk measuresSimulationsStatistical tests
Type
Papers
Information
Annals of Actuarial Science , Volume 11 , Issue 2 , September 2017 , pp. 237 - 252
Copyright
© Institute and Faculty of Actuaries 2016 

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