ρ-arbitrage and ρ-consistent pricing for star-shaped risk measures

Mathematics of Operations Research

35 Pages Posted: 11 Oct 2021 Last revised: 28 Feb 2024

See all articles by Martin Herdegen

Martin Herdegen

University of Warwick - Department of Statistics

Nazem Khan

University of Warwick - Department of Statistics

Date Written: September 17, 2021

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 weak sensitivity to large losses and show that it is key to ensure the existence of optimal portfolios. Second, we give primal and dual characterisations 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: portfolio selection, ρ-arbitrage, convex risk measures, star-shaped risk measures, dual characterisation, good-deals, ρ-consistent pricing

JEL Classification: G11, D81, C61

Suggested Citation

Herdegen, Martin and Khan, Nazem, ρ-arbitrage and ρ-consistent pricing for star-shaped risk measures (September 17, 2021). Mathematics of Operations Research , Available at SSRN: https://ssrn.com/abstract=3925492 or http://dx.doi.org/10.2139/ssrn.3925492

Martin Herdegen (Contact Author)

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

Nazem Khan

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

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