Maximum Spectral Measures of Risk with Given Risk Factor Marginal Distributions
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Publication:6118342
DOI10.1287/MOOR.2022.1299arXiv2010.14673OpenAlexW3094948588WikidataQ114058143 ScholiaQ114058143MaRDI QIDQ6118342
Author name not available (Why is that?)
Publication date: 23 February 2024
Published in: (Search for Journal in Brave)
Abstract: We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known, but whose joint distribution is unknown. The factors may take values in complete separable metric spaces. We introduce the notion of Maximum Spectral Measure (MSP), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSP admits a formulation as a solution to an optimization problem that has the same constraint set as the optimal transport problem, but with a more general objective function. We present results analogous to the Kantorovich duality, and we investigate the continuity properties of the optimal value function and optimal solution set with respect to perturbation of the marginal distributions. Additionally, we provide an asymptotic result characterizing the limiting distribution of the optimal value function when the factor distributions are simulated from finite sample spaces. The special case of Expected Shortfall and the resulting Maximum Expected Shortfall is also examined.
Full work available at URL: https://arxiv.org/abs/2010.14673
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