The risk-neutral non-additive probability with market frictions

نویسندگان

چکیده

Abstract The fundamental theory of asset pricing has been developed under the two main assumptions that markets are frictionless and have no arbitrage opportunities. In this case market enforces replicable assets valued by a linear function their payoffs, or as discounted expectation with respect to so-called risk-neutral probability. Important evidence presence frictions in financial led study rules such framework. Recently, Cerreia-Vioglio et al. (J Econ Theory 157:730–762, 2015) extended Fundamental Theorem Finance showing that, frictions, requiring put–call parity hold, together mild assumption translation invariance, is equivalent rule being represented Choquet nonadditive This paper continues characterizing important properties (unique) probability $$v_f$$ v f associated f , when it not assumed be subadditive. First, we show observed violation call–put parity, condition considered Chateauneuf (Math Financ 6:323–330, 1996) similar (2015), consistent existence bid-ask spreads. Second, balancedness —or equivalently non-vacuity its core—is characterized an arbitrage-free eliminates all opportunities can obtained splitting payoffs parts; moreover (nonempty) core consists additive probabilities below whose (standard) expectations . Third, strengthening again previous condition, strictly positive which allows recover standard formulation for markets.

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ژورنال

عنوان ژورنال: Economic Theory Bulletin

سال: 2022

ISSN: ['2196-1085', '2196-1093']

DOI: https://doi.org/10.1007/s40505-022-00216-4