Set optimization of set-valued risk measures

Elisa Mastrogiacomo () and Matteo Rocca
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Elisa Mastrogiacomo: Insubria University
Matteo Rocca: Insubria University

Annals of Operations Research, 2021, vol. 296, issue 1, No 12, 314 pages

Abstract: 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.

Keywords: Set-valued risk measures; Value at risk; Average value at risk; Portfolio optimization; Set-optimization; 91B30; 49J53; 46N10; 26E25 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10479-020-03541-8

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