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Multi-utility representations of incomplete preferences induced by set-valued risk measures


Munari, Cosimo (2021). Multi-utility representations of incomplete preferences induced by set-valued risk measures. Finance and Stochastics, 25(1):77-99.

Abstract

We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for representations that are both parsimonious (the family of representing functionals is indexed by a tractable set of parameters) and well behaved (the representing functionals satisfy nice regularity properties with respect to the structure of the underlying space of alternatives). The key to our results is a general dual representation of set-valued risk measures that unifies the existing dual representations in the literature and highlights their link with duality results for scalar risk measures.

Abstract

We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for representations that are both parsimonious (the family of representing functionals is indexed by a tractable set of parameters) and well behaved (the representing functionals satisfy nice regularity properties with respect to the structure of the underlying space of alternatives). The key to our results is a general dual representation of set-valued risk measures that unifies the existing dual representations in the literature and highlights their link with duality results for scalar risk measures.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Finance
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Finance, Statistics and Probability
Scope:Discipline-based scholarship (basic research)
Language:English
Date:1 January 2021
Deposited On:24 Aug 2021 16:50
Last Modified:25 Jun 2024 01:42
Publisher:Springer
ISSN:0949-2984
OA Status:Hybrid
Free access at:Official URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s00780-020-00440-5
Related URLs:https://link.springer.com/article/10.1007/s00780-020-00440-5
Other Identification Number:merlin-id:20473
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)