Abstract.
Let \({\cal Q}\) be the set of equivalent martingale measures for a given process \(S\), and let \(X\) be a process which is a local supermartingale with respect to any measure in \({\cal Q}\). The optional decomposition theorem for \(X\) states that there exists a predictable integrand \(\varphi\) such that the difference \(X-\varphi\cdot S\) 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.
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Föllmer, H., Kabanov, Y. Optional decomposition and Lagrange multipliers. Finance Stochast 2, 69–81 (1997). https://doi.org/10.1007/s007800050033
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DOI: https://doi.org/10.1007/s007800050033