FIRST ORDER BSPDEs IN HIGHER DIMENSION FOR OPTIMAL CONTROL PROBLEMS
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Dokuchaev, N. 2017. First Order BSPDEs in Higher Dimension for Optimal Control Problems. SIAM Journal on Control and Optimization. 55 (2): pp. 818-834.
SIAM Journal on Control and Optimization
Department of Mathematics and Statistics
Copyright © 2017 Society for Industrial and Applied Mathematics
This paper studies the first order backward stochastic partial differential equations suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogues of Hamilton--Jacobi--Bellman equations and allow one to construct the value function for stochastic optimal control problems with unspecified dynamics where the underlying processes do not necessarily satisfy stochastic differential equations of a known kind with a given structure. The problems considered arise in financial modeling.
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