Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/304450 
Year of Publication: 
2024
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 694
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
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.
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Working Paper

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