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Bounds on Choquet risk measures in finite product spaces with ambiguous marginals

Author

Listed:
  • Ghossoub Mario
  • Saunders David

    (Department of Statistics and Actuarial Science, University of Waterloo, 200 University Ave. W., Waterloo, ON N2L 3G1, Canada)

  • Zhang Kelvin Shuangjian

    (Department of Statistics and Actuarial Science, University of Waterloo, 200 University Ave. W., Waterloo, ON N2L 3G1, Canada)

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.

Suggested Citation

  • Ghossoub Mario & Saunders David & Zhang Kelvin Shuangjian, 2024. "Bounds on Choquet risk measures in finite product spaces with ambiguous marginals," Statistics & Risk Modeling, De Gruyter, vol. 41(1-2), pages 49-72, January.
    • Handle: RePEc:bpj:strimo:v:41:y:2024:i:1-2:p:49-72:n:1
    DOI: 10.1515/strm-2023-0006
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