Kebiri, O. and Neureither, L. and Hartmann, C. (2018) Singularly perturbed forwardbackward stochastic differential equations: application to the optimal control of bilinear systems. Computation . (Submitted)

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Official URL: http://arxiv.org/abs/1802.04978
Abstract
We study linearquadratic stochastic optimal control problems with bilinear state dependence for which the underlying stochastic differential equation (SDE) consists of slow and fast degrees of freedom. We show that, in the same way in which the underlying dynamics can be well approximated by a reduced order effective dynamics in the time scale limit (using classical homogenziation results), the associated optimal expected cost converges in the time scale limit to an effective optimal cost. This entails that we can well approximate the stochastic optimal control for the whole system by the reduced order stochastic optimal control, which is clearly easier to solve because of lower dimensionality. The approach uses an equivalent formulation of the HamiltonJacobiBellman (HJB) equation, in terms of forwardbackward SDEs (FBSDEs). We exploit the efficient solvability of FBSDEs via a least squares Monte Carlo algorithm and show its applicability by a suitable numerical example.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint in SciRate.arXiv:1802.04978 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  2222 
Deposited By:  Silvia Hoemke 
Deposited On:  16 Feb 2018 15:50 
Last Modified:  16 Feb 2018 15:50 
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