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

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Mathematics of Operations Research Pub Date : 2024-07-09 DOI:10.1287/moor.2023.0173

Martin Herdegen, Nazem Khan

引用次数: 0

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.

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星形风险度量的 ρ 套利和 ρ 一致性定价

本文重新探讨了单期金融市场中的均值风险投资组合选择，其中风险由星形风险度量 ρ 量化。首先，我们引入了对大预期损失敏感的新公理，并证明它是确保最优投资组合存在的关键。其次，我们给出了（强）ρ套利的基本特征和对偶特征。最后，我们利用不存在（强）ρ套利的条件明确推导出外部金融合约的（强）ρ一致价格区间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics of Operations Research 管理科学-应用数学

CiteScore

3.40

自引率

5.90%

发文量

178

审稿时长

15.0 months

期刊介绍： Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.