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Set optimization of set-valued risk measures

  • S.I.: MOPGP 2017
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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.

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Acknowledgements

The authors wish to thank the referees for their reports, that helped to improve the research, and, hopefully, will lead to further development in the future.

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  1. Department of Economics, Insubria University, Varese, Italy

    Elisa Mastrogiacomo & Matteo Rocca

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  1. Elisa Mastrogiacomo
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  2. Matteo Rocca
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Correspondence to Elisa Mastrogiacomo.

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Mastrogiacomo, E., Rocca, M. Set optimization of set-valued risk measures. Ann Oper Res 296, 291–314 (2021). https://doi.org/10.1007/s10479-020-03541-8

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