Summary.
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 different classes of equivalent measures. As an application, we extend results of Karatzas and Cvitanić [3] on hedging problems with constrained portfolios.
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Received: 6 August 1996/In revised form: 5 March 1997
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Föllmer, H., Kramkov, D. Optional decompositions under constraints. Probab Theory Relat Fields 109, 1–25 (1997). https://doi.org/10.1007/s004400050122
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DOI: https://doi.org/10.1007/s004400050122