A fast algorithm for the two dimensional HJB equation of stochastic control

Abstract : This paper analyses the implementation of the generalized finite differences method for the HJB equation of stochastic control, introduced by two of the authors in [Bonnans and Zidani, SIAM J. Numer. Anal. 41 (2003) 1008-1021]. The computation of coefficients needs to solve at each point of the grid (and for each control) a linear programming problem. We show here that, for two dimensional problems, this linear programming problem can be solved in O(p max) operations, where p max is the size of the stencil. The method is based on a walk on the Stern-Brocot tree, and on the related filling of the set of positive semidefinite matrices of size two.
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Submitted on : Wednesday, May 7, 2014 - 5:07:55 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM

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Frédéric Bonnans, Elisabeth Ottenwaelter, Hasnaa Zidani. A fast algorithm for the two dimensional HJB equation of stochastic control. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2004, 38 (4), pp.723-735. ⟨10.1051/m2an:2004034⟩. ⟨hal-00988282⟩

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