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

2022/02/15 by Martin Herdegen, Herdegen, Martin, Nazem Khan +1 · 3 citations
Decision Sciences · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2202.07610

openalex publication_date 2022/02/15 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

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 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.

Cited by

• When risk defies order: On the limits of fractional stochastic dominance
• The Interplay between Utility and Risk in Portfolio Selection
• Lambda Expected Shortfall

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