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
Motivated by a hedging problem in mathematical finance, El Karoui and Quenez  and Kramkov  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  on hedging problems with constrained portfolios.
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