Arbitrage Pricing in Convex, Cash-Additive Markets

Emy Lécuyer, Frank Riedel and Lorenzo Stanca
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Emy Lécuyer: Center for Mathematical Economics, Bielefeld University
Frank Riedel: Center for Mathematical Economics, Bielefeld University
Lorenzo Stanca: Center for Mathematical Economics, Bielefeld University

No 694, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We consider superhedging and no-arbitrage pricing in markets with a convex and cash-additive structure and derive an explicit functional form for the super-replication price. Using convex duality methods, we show that the superhedging price maximizes the difference between the expected payoff and a confidence function that accounts for the reliability of the probability used in pricing. We demonstrate that the existence of a strictly positive probability within the domain of the confidence function, which maximizes the super-replication price for a specific payoff and acts as a lower bound for all other payoffs, is necessary and sufficient to prevent arbitrage opportunities. Furthermore, we explore entropy pricing as a notable example of a super-replication pricing functional and provide conditions on the market structure under which the super-replication price takes the form of entropy pricing. We show that the confidence function in entropy pricing can be expressed using the Kullback-Leibler divergence.

Pages: 25
Date: 2024-10-09
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