ρ -Arbitrage and ρ -Consistent Pricing for Star-Shaped Risk Measures

Martin Herdegen () and Nazem Khan ()
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Martin Herdegen: Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom
Nazem Khan: School of Mathematics, Dublin City University, Dublin D09 FW22, Ireland

Mathematics of Operations Research, 2025, vol. 50, issue 2, 1555-1583

Abstract: This paper revisits mean-risk portfolio selection in a one-period financial market, where risk is quantified by a star-shaped risk measure ρ . We make three contributions. First, we introduce the new axiom of sensitivity to large expected losses and show that it is key to ensure the existence of optimal portfolios. Second, we give primal and dual characterizations of (strong) ρ -arbitrage. Finally, we use our conditions for the absence of (strong) ρ -arbitrage to explicitly derive the (strong) ρ -consistent price interval for an external financial contract.

Keywords: 91G10; 90C46; portfolio selection; ρ -arbitrage; convex risk measures; star-shaped risk measures; dual characterization; good-deals; ρ -consistent pricing (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:2:p:1555-1583

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