Article ID Journal Published Year Pages File Type
5076872 Insurance: Mathematics and Economics 2013 8 Pages PDF
Abstract

•A multivariate generalized beta distribution is presented for positive losses.•Marginals follow a second kind beta distribution and can be are heavy-tailed.•Sums of dependent losses are easily derived in this model.•Risk measures for the sum of marginals have simple expressions.•Spreadsheet calculation is illustrated using operational risk data.

Closed-form expressions for basic risk measures, such as value-at-risk and tail value-at-risk, are given for a family of statistical distributions that are specially suitable for right-skewed positive random variables. This is useful for risk aggregation in many insurance and financial applications that model positive losses, where the Gaussian assumption is not valid. Our results provide a direct and flexible parametric approach to multivariate risk quantification, for sums of correlated positive loss distributions, that can be readily implemented in a spreadsheet.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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