Optimal capital allocation with copulas

In this paper, we investigate optimal capital allocation problems for a portfolio consisting of different lines of risks linked by a Farlie-Gumbel- Morgenstern copula, modelling the dependence between them. Based on the Tail Mean-Variance principle, we examine the bivariate case and then the multivariate case. Explicit formulae for optimal capital allocations are obtained for exponential loss distributions. Finally, the results are illustrated by various numerical examples.