Optional decompositions under constraints

Hans Föllmer and D. O. Kramkov

No 1997,31, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: Motivated by a hedging problem in mathematical finance, El Karoui and Quenez [7] and Kramkov [14] have developed optional versions of the Doob-Meyer decomposition which hold simultaneously for all equivalent martingale measures. We investigate the general structure of such optional decompositions, both in additive and in multiplicative form, and under constraints corresponding to di_erent classes of equivalent measures. As an application, we extend results of Karatzas and Cvitanic [3] on hedging problems with constrained portfolios.

Date: 1997
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