Convex Duality and Generalized Solutions in Optimal Control Problem for Stopped Processes

SICON, Vol. 30, No. 2, March 1992

Posted: 10 Jan 2006 Last revised: 20 Nov 2007

See all articles by Steven H. Zhu

Steven H. Zhu

Banc of America Merrill Lynch; Morgan Stanley

Abstract

The approach consists of imbedding the original control problem tightly in a convex mathematical programming problem on the space of measures and then solving the latter problem by duality in convex analysis. The dual to the control problem is to find the supremum of all smooth subsolutions to the Bellman equation. Because of the effect of stops at the boundary of the domain, a different formulation of strong and weak problems will be adopted to make use of the convex duality method. The results about the decomposition of weak measures provide a clear intepretation for such a effect in the weak formualtion of our control problem.

Keywords: Optimal control, stopped processes, smooth subsolution, convex duality, strong and weak problems

JEL Classification: C44

Suggested Citation

Zhu, Steven H., Convex Duality and Generalized Solutions in Optimal Control Problem for Stopped Processes. SICON, Vol. 30, No. 2, March 1992. Available at SSRN: https://ssrn.com/abstract=874287

Steven H. Zhu (Contact Author)

Banc of America Merrill Lynch ( email )

Bank of America Plaza
335 Madison Ave, 5th Floor
New York, NY 10017
United States
646-855-1853 (Phone)

HOME PAGE: http://www.riskwhoswho.com/Charter-Members.html

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

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