NEW: Arbitrage Pricing in Convex, Cash-Additive Markets

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.