Generalized Duality for Model-Free Superhedging given Marginals

Arash Fahim; Yu-Jui Huang; Saeed Khalili

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arXiv · 1909.06036

Generalized Duality for Model-Free Superhedging given Marginals

Arash Fahim·Yu-Jui Huang·Saeed Khalili

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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.

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Arash Fahim, Yu-Jui Huang, Saeed Khalili. 2019-09-13. Generalized Duality for Model-Free Superhedging given Marginals. https://arxiv.org/abs/1909.06036

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