Journal article
Bounds on Choquet risk measures in finite product spaces with ambiguous marginals
Statistics & risk modeling, Vol.41(1-2), pp.49-72
01/01/2024
DOI: 10.1515/strm-2023-0006
Abstract
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures on the marginal spaces and the joint nonadditive distribution on the product space is unknown. We treat this problem as a generalization of the optimal transport problem to the setting of nonadditive measures. We provide explicit characterizations of the optimal solutions for finite marginal spaces, and we investigate some of their properties. We further discuss the connections with linear programming, showing that the optimal transport problems for capacities are linear programs, and we also characterize their duals explicitly. Finally, we investigate a series of numerical examples, including a comparison with the classical optimal transport problem, and applications to counterparty credit risk.
Details
- Title: Subtitle
- Bounds on Choquet risk measures in finite product spaces with ambiguous marginals
- Creators
- Mario Ghossoub - University of WaterlooDavid Saunders - University of WaterlooKelvin Shuangjian Zhang - University of Waterloo
- Resource Type
- Journal article
- Publication Details
- Statistics & risk modeling, Vol.41(1-2), pp.49-72
- DOI
- 10.1515/strm-2023-0006
- ISSN
- 2193-1402
- eISSN
- 2196-7040
- Publisher
- Walter De Gruyter
- Number of pages
- 24
- Grant note
- Natural Sciences and Engineering Research Council of Canada; Natural Sciences and Engineering Research Council of Canada (NSERC); CGIAR
- Language
- English
- Date published
- 01/01/2024
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9985179682302771
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