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MORE ON MINIMAL ENTROPY–HELLINGER MARTINGALE MEASURE
Author(s) -
Choulli Tahir,
Stricker Christophe
Publication year - 2006
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.1467-9965.2006.00258.x
Subject(s) - mathematics , pointwise , local martingale , martingale (probability theory) , hellinger distance , doob's martingale inequality , martingale pricing , entropy (arrow of time) , mathematical economics , econometrics , mathematical analysis , physics , thermodynamics
This paper extends our recent paper (Choulli and Stricker 2005) to the case when the discounted stock price process may be unbounded and may have predictable jumps. In this very general context, we provide mild necessary conditions for the existence of the minimal entropy–Hellinger local martingale density and we give an explicit description of this extremal martingale density that can be determined by pointwise solution of equations in depending only on the local characteristics of the discounted price process S . The uniform integrability and other integrability properties are investigated for this extremal density, which lead to the conditions of the existence of the minimal entropy–Hellinger martingale measure. Finally, we illustrate the main results of the paper in the case of a discrete‐time market model, where the relationship of the obtained optimal martingale measure to a dynamic risk measure is discussed.