Risk capital decomposition for a multivariate dependent gamma portfolio

This paper examines the tail conditional expectation risk measure (TCE) in the case of a multivariate gamma portfolio of risks. Explicit formulas for both the TCE and the risk capital allocations based on it are provided in the context of the multivariate model possessing dependent gamma marginals. Some of our results exceed the frameworks of the multivariate gamma distributions and may be applied to other non-negative risks.