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Authors: Stephan E. Ludwig 1 ; Justin A. Sirignano 2 ; Ruojun Huang 2 and George Papanicolaou 2

Affiliations: 1 Heidelberg University, Germany ; 2 Stanford University, United States

ISBN: 978-989-8425-97-3

Keyword(s): Optimal stochastic control, Stochastic maximum principle, Forward-Backward stochastic differential equations.

Abstract: An algorithm for solving continuous-time stochastic optimal control problems is presented. The numerical scheme is based on the stochastic maximum principle (SMP) as an alternative to the widely studied dynamic programming principle (DDP). By using the SMP, (Peng, 1990) obtained a system of coupled forward-backward stochastic differential equations (FBSDE) with an external optimality condition. We extend the numerical scheme of (Delarue and Menozzi, 2006) by a Newton-Raphson method to solve the FBSDE system and the optimality condition simultaneously. As far as the authors are aware, this is the first fully explicit numerical scheme for the solution of optimal control problems through the solution of the corresponding extended FBSDE system. We discuss possible numerical advantages to the DDP approach and consider an optimal investment-consumption problem as an example.

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Paper citation in several formats:
E. Ludwig, S.; A. Sirignano, J.; Huang, R. and Papanicolaou, G. (2012). A FORWARD-BACKWARD ALGORITHM FOR STOCHASTIC CONTROL PROBLEMS - Using the Stochastic Maximum Principle as an Alternative to Dynamic Programming.In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8425-97-3, pages 83-89. DOI: 10.5220/0003885900830089

@conference{icores12,
author={Stephan E. Ludwig. and Justin A. Sirignano. and Ruojun Huang. and George Papanicolaou.},
title={A FORWARD-BACKWARD ALGORITHM FOR STOCHASTIC CONTROL PROBLEMS - Using the Stochastic Maximum Principle as an Alternative to Dynamic Programming},
booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2012},
pages={83-89},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003885900830089},
isbn={978-989-8425-97-3},
}

TY - CONF

JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - A FORWARD-BACKWARD ALGORITHM FOR STOCHASTIC CONTROL PROBLEMS - Using the Stochastic Maximum Principle as an Alternative to Dynamic Programming
SN - 978-989-8425-97-3
AU - E. Ludwig, S.
AU - A. Sirignano, J.
AU - Huang, R.
AU - Papanicolaou, G.
PY - 2012
SP - 83
EP - 89
DO - 10.5220/0003885900830089

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