Comparing the riskiness of dependent portfolios via nested L-statistics

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.

Beyond the Pearson Correlation: Heavy-Tailed Risks, Weighted Gini Correlations, and a Gini-Type Weighted Insurance Pricing Model

“…Several works have appeared since the monograph of Yitzhaki and Schechtman (2013) that tackle Gini-type covariances and other quantities of interest in actuarial and financial applications. For example, Frees et al (2014) and Samanthi et al (2017) develop Gini-based methods designed for insurance ratemaking and for assessing the riskiness of portfolios. Gini-type covariances, called Gini autocovariances, have recently been introduced and used when analyzing heavytailed time series.…”

Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions

“…In particular, they illustrate such effects by using standard model selection tools such as Akaike Information Criterion to determine the "best" regression subset of covariates, and then apply the selected model for claim prediction. Bignozzi et al (2015) and Samanthi et al (2017) are two recent examples of theoretical and practical investigations, respectively, of the effects of the data dependence assumption on subsequent risk measuring. Also, an extensive simulation study involving estimation of upper quantiles of lognormal, log-logistic, and log-double exponential distributions under model and parameter uncertainty was conducted by Modarres et al (2002).…”