Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5076872 | Insurance: Mathematics and Economics | 2013 | 8 Pages |
â¢A multivariate generalized beta distribution is presented for positive losses.â¢Marginals follow a second kind beta distribution and can be are heavy-tailed.â¢Sums of dependent losses are easily derived in this model.â¢Risk measures for the sum of marginals have simple expressions.â¢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.