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Time-average control of martingale problems: A linear programming formulation. (English) Zbl 0699.49019

Summary: This paper studies the average cost for controlled systems given as solutions of the martingale problem for their generator. The control problem is reformulated as a linear programming problem and conditions are given for the existence of an optimal solution. It is further shown that the optimal control can be taken to depend only on the history of the system and that this cost remains optimal for systems with different initial distributions.

MSC:

49J55 Existence of optimal solutions to problems involving randomness
93E20 Optimal stochastic control
90C90 Applications of mathematical programming
90C05 Linear programming
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