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A COUNTEREXAMPLE CONCERNING THE VARIANCE‐OPTIMAL MARTINGALE MEASURE
Author(s) -
Černý Aleš,
Kallsen Jan
Publication year - 2008
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.1467-9965.2007.00334.x
Subject(s) - martingale (probability theory) , local martingale , mathematics , martingale pricing , counterexample , martingale difference sequence , doob's martingale inequality , measure (data warehouse) , econometrics , mathematical economics , discrete mathematics , computer science , database
The present note addresses an open question concerning a sufficient characterization of the variance‐optimal martingale measure. Denote by S the discounted price process of an asset and suppose that Q ★ is an equivalent martingale measure whose density is a multiple of 1 −ϕ· S T for some S ‐integrable process ϕ. We show that Q ★ does not necessarily coincide with the variance‐optimal martingale measure, not even if ϕ· S is a uniformly integrable Q ★ ‐martingale.