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Set optimization of set-valued risk measures

Author

Listed:
  • Elisa Mastrogiacomo

    (Insubria University)

  • Matteo Rocca

    (Insubria University)

Abstract

A new approach to optimizing or hedging a portfolio of financial instruments to reduce risk is presented. Central to this approach are concepts and tools of set-optimization theory. It focuses on the problem of minimizing set-valued risk measures applied to portfolios. We present sufficient conditions for the existence of solutions of a set-valued risk minimization problem under some semi-continuity assumption. The methodology is applied to the optimization of set-valued Value at Risk and Average Value at Risk. Two examples at the end illustrate various features of the theoretical construction, among them the geometry of the image sets.

Suggested Citation

  • Elisa Mastrogiacomo & Matteo Rocca, 2021. "Set optimization of set-valued risk measures," Annals of Operations Research, Springer, vol. 296(1), pages 291-314, January.
    • Handle: RePEc:spr:annopr:v:296:y:2021:i:1:d:10.1007_s10479-020-03541-8
    DOI: 10.1007/s10479-020-03541-8
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    References listed on IDEAS

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