Simple risk measure calculations for sums of positive random variables

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...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2013-07, Vol.53 (1), p.273-280
Main Authors: Guillén, Montserrat, Sarabia, José María, Prieto, Faustino
Format: Article
Language:English
Subjects:
Beta distribution
Economic calculations
Heavy-tailed
Insurance
Measurement
Multivariate analysis
Multivariate loss models
Normal distribution
Random variables
Risk
Risk assessment
Studies
Tail value at risk
Value at risk
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Summary: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. •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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2013.05.007