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Optimal expected-shortfall portfolio selection with copula-induced dependence. (English) Zbl 1418.91469

Summary: We provide a computational framework for the selection of weights \((\omega_1,\dots,\omega_d)\) that minimize the expected shortfall of the aggregated risk \(Z=\sum^d_{i=1} \omega_i X_i\). Contrary to classic and recent results, we neither restrict the marginal distributions nor the dependence structure of \((X_1,\dots,X_d)\) 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.

MSC:

91G10 Portfolio theory
62P05 Applications of statistics to actuarial sciences and financial mathematics
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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