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Robust FTAP and superhedging in discrete time

Banff International Research Station for Mathematical Innovation and Discovery

We study robust pricing and hedging in a general discrete time setup with dynamic trading in risky assets and static trading in finitely many options with given initial prices. We allow to express modelling beliefs by specifying a (universally measurable) subset of feasible paths. We establish a robust FTAP: absence of robust (model-independent) arbitrage is equivalent to existence of a martingale measure calibrated to the given option prices. The arbitrage here corresponds to the situation when all agents agree that there is an arbitrage albeit they might disagree as to how to realise it. The arbitrage strategy is measurable with respect to a larger filtration which aggregates these views but, at the same time, does not perturb the structure of martingale measures. Our proof is iterative and uses a robust pricing-hedging duality which we also establish. (This work builds on earlier contributions by Burzoni, Frittelli and Maggis (2015) and is a joint work with Burzoni, Frittelli, Hou and Maggis.)

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes

video/mp4

Author affiliation: University of Oxford

2017-01-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59771

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/