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LOWER AND UPPER BOUNDS OF MARTINGALE MEASURE DENSITIES IN CONTINUOUS TIME MARKETS
Author(s) -
Di Nunno Giulia,
Baadshaug Eide Inga
Publication year - 2011
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/j.1467-9965.2010.00442.x
Subject(s) - martingale (probability theory) , mathematics , mathematical economics , local martingale , upper and lower bounds , measure (data warehouse) , axiom , martingale pricing , economics , computer science , mathematical analysis , geometry , database
In a continuous time market model we consider the problem of existence of an equivalent martingale measure with density lying within given lower and upper bounds and we characterize a necessary and sufficient condition for this. In this sense our main result can be regarded as a version of the fundamental theorem of asset pricing. In our approach we suggest an axiomatic description of prices on L p ‐spaces (with p ∈[1, ∞)) and we rely on extension theorems for operators.