Optional Decomposition and Lagrange Multipliers
Finance and Stochastics, Vol 2 No 1, 1998
Posted: 21 Apr 1998
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
Do you have a job opening that you would like to promote on SSRN?
Feedback to SSRN
If you need immediate assistance, call 877-SSRNHelp (877 777 6435) in the United States, or +1 212 448 2500 outside of the United States, 8:30AM to 6:00PM U.S. Eastern, Monday - Friday.