Ordering Gini indexes of multivariate elliptical risks

Samanthi, Ranadeera Gamage Madhuka; Wei, Wei; Brazauskas, Vytaras

doi:10.1016/j.insmatheco.2016.03.005

Cited by 9 publications

(8 citation statements)

References 19 publications

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“…Some preliminary results on this topic are reported by Samanthi et al . (2016). Third, a natural extension of the test is to redesign it for discontinuous data that may include excessive number of zeros, but otherwise are continuous.…”

Section: Discussionmentioning

confidence: 99%

Comparing the riskiness of dependent portfolios via nested L-statistics

2016

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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.

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Section: Discussionmentioning

confidence: 99%

Comparing the riskiness of dependent portfolios via nested L-statistics

2016

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“…Since Corrado Gini introduced an index to measure concentration or inequality of incomes (see Gini (1936), for English translation of the original article), it has been studied extensively because of its importance in many fields such as economics, actuarial science, finance, operations research, queuing theory and statistics; see, for example, Denuit et Recently, there is a growing interest in the study and applications of the Gini index; See e.g. Samanthi, Wei and Brazauskas (2016), and the references therein. Let X = (X 1 , ..., X n ) be n portfolios of risks or random variables, these portfolios can be independent or dependent.…”

Section: Introductionmentioning

confidence: 99%

“…For example, for the ordering of Gini indexes of multivariate normal risks, Samanthi et al (2016) proposed the following conjecture.…”

Section: Introductionmentioning

confidence: 99%

“…

In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the monotonicity of the Gini index in the usual stochastic order and increasing convex order proposed by Samanthi, Wei and Brazauskas (2016) and are also suitable for multivariate elliptical risks. We also study the tail probability of Gini index for multivariate elliptical risks and revised a large deviation result for the Gini indexes of multivariate normal risks in .

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Stochastic ordering of Gini indexes for multivariate elliptical random variables

Yin¹

2019

Preprint

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“…cit. (also, Samanthi et al, 2016). For example, we learn that when the pair (X, L) follows the bivari-…”

Section: Introductionmentioning

confidence: 99%

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

Furman

Zitikis²

2017

ASTIN Bull.

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Gini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations, naturally, the classical Pearson correlation coefficient is of little use. On the other hand, it has been observed that when light-tailed situations are of interest, and hence when both the Gini-type and Pearson correlation coefficients are well-defined and finite, then these coefficients are related and sometimes even coincide. In general, understanding how the correlation coefficients above are related has been an illusive task. In this paper we put forward arguments that establish such a connection via certain regressiontype equations. This, in turn, allows us to introduce a Gini-type Weighted Insurance Pricing Model that works in heavy-tailed situation and thus provides a natural alternative to the classical Capital Asset Pricing Model. We illustrate our theoretical considerations using several bivariate distributions, such as elliptical and those with heavy-tailed Pareto margins.

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Ordering Gini indexes of multivariate elliptical risks

Cited by 9 publications

References 19 publications

Comparing the riskiness of dependent portfolios via nested L-statistics

Comparing the riskiness of dependent portfolios via nested L-statistics

Stochastic ordering of Gini indexes for multivariate elliptical random variables

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

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