Optional Decomposition and Lagrange Multipliers
Finance and Stochastics, Vol 2 No 1, 1998
Posted: 21 Apr 1998
Abstract
Let 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 Q. The optional decomposition theorem for X states that there exists a predictable integrand phi such that the difference X-phi times 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.
JEL Classification: G10, G12
Suggested Citation: Suggested Citation
Follmer, Hans and Kabanov, Youri, Optional Decomposition and Lagrange Multipliers. Finance and Stochastics, Vol 2 No 1, 1998, Available at SSRN: https://ssrn.com/abstract=78448
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