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The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets[Note 1. I am very grateful to an anonymous referee for ...]
Author(s) -
Frittelli Marco
Publication year - 2000
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 - 10.1111/1467-9965.00079
Subject(s) - martingale pricing , economics , martingale (probability theory) , incomplete markets , econometrics , mathematical economics , local martingale , doob's martingale inequality , mathematics , valuation (finance) , financial economics , microeconomics , finance
Let χ be a family of stochastic processes on a given filtered probability space (Ω, F , ( F t ) t ∈ T , P ) with T ⊆R + . Under the assumption that the set M e of equivalent martingale measures for χ is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure that minimizes the relative entropy, with respect to P , in the class of martingale measures. We then provide the characterization of the density of the minimal entropy martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy.