- Published 2016 in Finance and Stochastics

The approach to pricing and hedging of options through considering the dual problem of finding the expected value of the payoff under a risk-neutral measure is both classical and well understood. In a complete market setting it is simply the way to compute the hedging price, as argued by Black and Scholes [4]. In incomplete markets, the method originated in El Karoui and Quenez [16], culminating in the seminal work of Delbaen and Schachermayer [14]. Almost as classical is the problem of finding superhedging prices under various constraints on the set of admissible portfolios. Questions of this type arise in Cvitanić and Karatzas [11], where convex constraints in the hedging problem lead to a dual problem where one looks for the largest expectation of the payoff of the derivative in a class of auxiliary markets, where the auxiliary markets are a modification of the original markets reflecting the trading constraints. In the special case of markets where participants may not short sell assets, the class of auxiliary markets correspond to the class of supermartingale measures. (For further results in this direction, see e.g. Jouini and Kallal [26]; Cvitanić et al. [12]; Pham and Touzi [32]; Pulido [34].)

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@article{Cox2016RobustPA,
title={Robust pricing and hedging under trading restrictions and the emergence of local martingale models},
author={Alexander M. G. Cox and Zhaoxu Hou and Jan Obl{\'o}j},
journal={Finance and Stochastics},
year={2016},
volume={20},
pages={669-704}
}