We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Maximum Spectral Measures of Risk with Given Risk Factor Marginal Distributions.
- Authors
Ghossoub, Mario; Hall, Jesse; Saunders, David
- 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 (MSM), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSM 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. Funding: M. Ghossoub and D. Saunders acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada in the form of Discovery Grants [Grants 2018-03961 and 2017-04220, respectively].
- Subjects
CANADA; MARGINAL distributions; METRIC spaces; NONLINEAR functions; VALUATION of real property; GRANTS (Money)
- Publication
Mathematics of Operations Research, 2023, Vol 48, Issue 2, p1158
- ISSN
0364-765X
- Publication type
Article
- DOI
10.1287/moor.2022.1299