%AMcEneaney, William%ADower, Peter%D2020%I
%K
%MOSTI ID: 10171200
%PMedium: X
%TConversion of Certain Stochastic Control Problems into Deterministic Control
Problems
%XA class of nonlinear, stochastic staticization control problems (including minimization problems with smooth, convex, coercive payoffs) driven by diffusion dynamics with constant diffusion coefficient is considered. A fundamental solution form is obtained where the same solution can be used for a limited variety of terminal costs without re-solution of the problem. One may convert this fundamental solution form from a stochastic control problem form to a deterministic control problem form. This yields an equivalence between certain second-order (in space) Hamilton-Jacobi partial differential equations (HJ PDEs) and associated first-order HJ PDEs. This reformulation has substantial numerical implications.
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