Generalized Duality for Model-Free Superhedging given Marginals
Abstract
In a discrete-time financial market, a generalized duality is established for model-free superhedging, given marginal distributions of the underlying asset. Contrary to prior studies, we do not require contingent claims to be upper semicontinuous, allowing for upper semi-analytic ones. The generalized duality stipulates an extended version of risk-neutral pricing. To compute the model-free superhedging price, one needs to find the supremum of expected values of a contingent claim, evaluated not directly under martingale (risk-neutral) measures, but along sequences of measures that converge, in an appropriate sense, to martingale ones. To derive the main result, we first establish a portfolio-constrained duality for upper semi-analytic contingent claims, relying on Choquet's capacitability theorem. As we gradually fade out the portfolio constraint, the generalized duality emerges through delicate probabilistic estimations.
Keywords
Cite
@article{arxiv.1909.06036,
title = {Generalized Duality for Model-Free Superhedging given Marginals},
author = {Arash Fahim and Yu-Jui Huang and Saeed Khalili},
journal= {arXiv preprint arXiv:1909.06036},
year = {2019}
}