Gini-type measures of risk and variability: Gini shortfall,capital allocations,and heavy-tailed risks |
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| Affiliation: | 1. Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 5A7, Canada;3. Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada |
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| Abstract: | We introduce and explore Gini-type measures of risk and variability, and develop the corresponding economic capital allocation rules. The new measures are coherent, additive for co-monotonic risks, convenient computationally, and require only finiteness of the mean. To elucidate our theoretical considerations, we derive closed-form expressions for several parametric families of distributions that are of interest in insurance and finance, and further apply our findings to a risk portfolio of a bancassurance company. |
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