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$\rho$-arbitrage and $\rho$-consistent pricing for star-shaped risk measures

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  • Martin Herdegen
  • Nazem Khan

Abstract

This paper revisits mean-risk portfolio selection in a one-period financial market, where risk is quantified by a star-shaped risk measure $\rho$. 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) $\rho$-arbitrage. Finally, we use our conditions for the absence of (strong) $\rho$-arbitrage to explicitly derive the (strong) $\rho$-consistent price interval for an external financial contract.

Suggested Citation

  • Martin Herdegen & Nazem Khan, 2022. "$\rho$-arbitrage and $\rho$-consistent pricing for star-shaped risk measures," Papers 2202.07610, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2202.07610
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    Cited by:

    1. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.
    2. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2022. "Star-Shaped deviations," Papers 2207.08613, arXiv.org.

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