Robust Fundamental Theorem for Continuous Processes

25 Pages Posted: 19 Sep 2017

See all articles by Sara Biagini

Sara Biagini

LUISS University

Bruno Bouchard

Université Paris Dauphine - CEREMADE

Marcel Nutz

Columbia University

Date Written: October 2017

Abstract

We study a continuous‐time financial market with continuous price processes under model uncertainty, modeled via a family of possible physical measures. A robust notion 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: holds if and only if every admits a martingale measure that 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.

Keywords: fundamental theorem of asset pricing, arbitrage of the first kind, superhedging duality, nondominated model

Suggested Citation

Biagini, Sara and Bouchard, Bruno and Nutz, Marcel, Robust Fundamental Theorem for Continuous Processes (October 2017). Mathematical Finance, Vol. 27, Issue 4, pp. 963-987, 2017, Available at SSRN: https://ssrn.com/abstract=3039149 or http://dx.doi.org/10.1111/mafi.12110

Sara Biagini (Contact Author)

LUISS University ( email )

Viale Romania 32
Rome, 00197
Italy

Bruno Bouchard

Université Paris Dauphine - CEREMADE ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Marcel Nutz

Columbia University ( email )

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