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

• 成果类型: Article
• 署名作者: Herdegen, Martin; Khan, Nazem
• 署名单位: University of Warwick; Dublin City University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0173
• 发表日期: 2025
• 关键词: portfolio selection; optimization; shortfall; utility; bounds

摘要

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 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) 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.