Multivariate Tweedie Distributions and Some Related Capital-at-Risk Analysis

We study a multivariate extension of the univariate exponential dispersion Tweedie family of distributions. The class, referred to as the multi-variate Tweedie family (MTwF), on the one hand includes multivariate Poisson, gamma, inverse Gaussian, stable and compound Poisson distributions and on the other introduces a high variety of new dependent probabilistic models unstudied so far. We investigate various properties of MTwF and discuss its possible applications to financial risk management