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<p>Market frictions have motivated the development of nonlinear asset pricing models, as any departure from linearity in pricing reflects the presence of some form of friction. While sublinear pricing has been extensively studied, recent advances have extended the framework to encompass more general, and potentially nonconvex, pricing rules, most notably Choquet pricing. These developments raise foundational questions regarding the nature of arbitrage, which are central to this paper. In particular, relaxing the assumption of subadditivity introduces fundamental challenges. The set of admissible arbitrage opportunities broadens, allowing, for instance, multiple simultaneous buy-and-sell arbitrage opportunities that subadditivity would rule out by construction. These observations highlight the need for a generalized notion of arbitrage that operates under minimal assumptions, specifically, without relying on convexity, subadditivity, or even monotonicity of the pricing rule. This paper adresses these issues by taking the market pricing rule as a primitive concept, exogenously specified and defined axiomatically.</p>

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Pricing rules with market frictions: an axiomatic approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月8日

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  • Bernard Cornet

摘要

Market frictions have motivated the development of nonlinear asset pricing models, as any departure from linearity in pricing reflects the presence of some form of friction. While sublinear pricing has been extensively studied, recent advances have extended the framework to encompass more general, and potentially nonconvex, pricing rules, most notably Choquet pricing. These developments raise foundational questions regarding the nature of arbitrage, which are central to this paper. In particular, relaxing the assumption of subadditivity introduces fundamental challenges. The set of admissible arbitrage opportunities broadens, allowing, for instance, multiple simultaneous buy-and-sell arbitrage opportunities that subadditivity would rule out by construction. These observations highlight the need for a generalized notion of arbitrage that operates under minimal assumptions, specifically, without relying on convexity, subadditivity, or even monotonicity of the pricing rule. This paper adresses these issues by taking the market pricing rule as a primitive concept, exogenously specified and defined axiomatically.