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ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES
Author(s) -
Biagini Sara,
Bouchard Bruno,
Kardaras Constantinos,
Nutz Marcel
Publication year - 2017
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12110
Subject(s) - martingale (probability theory) , fundamental theorem of asset pricing , mathematical economics , arbitrage , local martingale , mathematics , martingale pricing , optional stopping theorem , simple (philosophy) , financial market , economics , econometrics , capital asset pricing model , arbitrage pricing theory , financial economics , finance , philosophy , epistemology
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 notionNA 1 ( 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:NA 1 ( P )holds if and only if every P ∈ P 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.