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 . 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) operations, where p 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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https://hal.inria.fr/inria-00071505
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Submitted on : Tuesday, May 23, 2006 - 5:47:36 PM
Last modification on : Friday, May 25, 2018 - 12:02:04 PM
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J. Frederic Bonnans, Elisabeth Ottenwaelter, Hasnaa Zidani. A fast algorithm for the two dimensional HJB equation of stochastic control. [Research Report] RR-5078, INRIA. 2004. ⟨inria-00071505⟩

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