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Robust Fundamental Theorem for Continuous Processes

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Date
2015
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1410.4962v2
Dewey
Economie financière
Sujet
Fundamental Theorem of Asset Pricing; Superhedging duality; Arbitrage of the Firs t Kind; Nondominated Model
JEL code
G12
Journal issue
Mathematical Finance
Publication date
2015
Publisher
Blackwell
DOI
http://dx.doi.org/10.1111/mafi.12110
URI
https://basepub.dauphine.fr/handle/123456789/14341
Collections
  • CEREMADE : Publications
Metadata
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Author
Biagini, Sara
Bouchard, Bruno
Kardaras, Constantinos
Nutz, Marcel
Type
Article accepté pour publication ou publié
Abstract (EN)
We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family inline image of possible physical measures. A robust notion inline image 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: inline image holds if and only if every inline image 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.

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