Abstract
In a continuous time setting, we consider a set of -absolutely continuous probability measures, containing at least one equivalent to , and denote by , the smallest m-stable closed convex set of probability measures containing . We shall prove mainly under the martingale representation property with respect to a continuous vector valued martingale S, that is the set of supermartingale measures for a family , where is a set of predictable vector valued processes. We state as an immediate consequence of Föllmer-Kramkov Theorem in H. Föllmer and D. Kramkov (Optional decompositions under constraints, Probab. Theory Relat. Fields 109 (1997), pp. 1–25), the decomposition of -supermartingales.
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