Generalized Duality for ModelFree Superhedging given Marginals
Abstract
In a discretetime financial market, a generalized duality is established for modelfree 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 semianalytic ones. The generalized duality stipulates an extended version of riskneutral pricing. To compute the modelfree superhedging price, one needs to find the supremum of expected values of a contingent claim, evaluated not directly under martingale (riskneutral) measures, but along sequences of measures that converge, in an appropriate sense, to martingale ones. To derive the main result, we first establish a portfolioconstrained duality for upper semianalytic contingent claims, relying on Choquet's capacitability theorem. As we gradually fade out the portfolio constraint, the generalized duality emerges through delicate probabilistic estimations.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 DOI:
 10.48550/arXiv.1909.06036
 arXiv:
 arXiv:1909.06036
 Bibcode:
 2019arXiv190906036F
 Keywords:

 Quantitative Finance  Pricing of Securities;
 Mathematics  Probability;
 60G42;
 91G20;
 91G80