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Deterministic and Stochastic Control Problems with Identical Optimal Cost Functions

Analysis and Optimization of Systems, A. Bensoussan and J. L. Lions (Eds.), Lecture Notes in Control and Information Sciences, Springer-Verlag, New York, 1988, 641-645

Posted: 17 Jun 2020

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased) ; State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

Date Written: 1988

Abstract

We consider two control problems on a finite horizon; one stochastic and the other deterministic. In both problems the running cost and the terminal cost are the same. The controllable input in both problems is of an additive nature with cost proportional to the input (which can be both positive and negatve, depending on the size of the input). The dynamics in the stochastic model is the same as that of the deterministic but with additional "noise" term. We show that the value functions in both problems are the same and the optimal policy for the stochastic problem is to keep the controlled process as close as possible to the optimal trajectory for the deterministic problem.

Keywords: Finite Horizon, Stochastic Model, Deterministic Problem

JEL Classification: C61, M11, M20

Suggested Citation

Sethi, Suresh and Taksar, Michael I., Deterministic and Stochastic Control Problems with Identical Optimal Cost Functions (1988). Analysis and Optimization of Systems, A. Bensoussan and J. L. Lions (Eds.), Lecture Notes in Control and Information Sciences, Springer-Verlag, New York, 1988, 641-645, Available at SSRN: https://ssrn.com/abstract=3608362

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased)

State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

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