Optimal Expected-Shortfall Portfolio Selection with Copula-Induced Dependence

We provide a computational framework for the selection of weights $$({\omega _1}, \ldots ,{\omega _d})$$(ω1,…,ωd) that minimize the expected shortfall of the aggregated risk $$Z = \mathop \sum \nolimits_{i = 1}^d {\omega _i}{X_i}$$Z=∑i=1dωiXi . Contrary to classic and recent results, we neither restrict the marginal distributions nor the dependence structure of $$({X_1}, \ldots ,{X_d})$$(X1,…,Xd) to any specific type. While the margins can be set to any absolutely continuous random variable with finite expectation, the dependence structure can be modelled by any absolutely continuous copula function. A real-world application to portfolio selection illustrates the usability of the new framework.