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Article Dans Une Revue Mathematical Finance Année : 2017

Robust Fundamental Theorem for Continuous Processes

Résumé

We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family P of possible physical measures. A robust notion NA1(P) of no-arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first main result is a version of the fundamental theorem of asset pricing: NA1(P) holds if and only if every P ∈ P admits a martingale measure which is equivalent up to a certain lifetime. The second main result provides the existence of optimal superhedging strategies for general contingent claims and a representation of the superhedging price in terms of martingale measures.
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Dates et versions

hal-01076062 , version 1 (21-10-2014)

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Sara Biagini, Bruno Bouchard, Constantinos Kardaras, Marcel Nutz. Robust Fundamental Theorem for Continuous Processes. Mathematical Finance, 2017, 27 (4), pp.963-987. ⟨10.1111/mafi.12110⟩. ⟨hal-01076062⟩
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