Institut für Mathematik, Humboldt Universit?t, Unter den Linden 6, D-10099 Berlin, Germany, DE Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow, RU
Abstract:
Let be the set of equivalent martingale measures for a given process , and let be a process which is a local supermartingale with respect to any measure in . The optional decomposition theorem for states that there exists a predictable integrand such that the difference is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional
analysis, and which removes any boundedness assumption.