Numerical solution of a long-term average control problem for singular stochastic processes

P. Kaczmarek, S. Kent, G. Rus, R. Stockbridge () and B. Wade

Mathematical Methods of Operations Research, 2007, vol. 66, issue 3, 473 pages

Abstract: This paper analyzes numerically a long-term average stochastic control problem involving a controlled diffusion on a bounded region. The solution technique takes advantage of an infinite-dimensional linear programming formulation for the problem which relates the stationary measures to the generators of the diffusion. The restriction of the diffusion to an interval is accomplished through reflection at one end point and a jump operator acting singularly in time at the other end point. Different approximations of the linear program are obtained using finite differences for the differential operators (a Markov chain approximation to the diffusion) and using a finite element method to approximate the stationary density. The numerical results are compared with each other and with dynamic programming. Copyright Springer-Verlag 2007

Keywords: Singular stochastic control; Stationary distribution; Long-term average; Finite element; Linear programming; Markov chain; 93E20; 93E25; 60G35 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s00186-007-0166-9

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