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Duality for pathwise superhedging in continuous time. (English) Zbl 1429.91314

The authors present a model-free pricing-hedging duality in continuous time for a frictionless market consisting of d risky assets. All price trajectories are assumed to be in a set, which is a \(\sigma \)-compact metric space. This allows to look at a price process as an d-dimensional canonical process. The superhedging problem is formulated with simple trading strategies, the claim is the limit inferior of continuous functions, which allows upper and lower semi-continuous claims, and superhedging is required in the pathwise sense. It is proved that the problem of finding the minimal superhedging price of a path-dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures, and under an additional not restrictive assumption to finding the supremum over all martingale measures with compact support. The relation with V. Vovk’s outer measure [Finance Stoch. 16, No. 4, 561–609 (2012; Zbl 1262.91163)] and semi-static superhedging with finitely many securities are also investigated. Interesting examples are given.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B24 Microeconomic theory (price theory and economic markets)
60G44 Martingales with continuous parameter

Citations:

Zbl 1262.91163
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References:

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