## 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.

Original language | English (US) |
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Title of host publication | ICORES 2012 - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems |

Pages | 83-89 |

Number of pages | 7 |

State | Published - 2012 |

Externally published | Yes |

Event | 1st International Conference on Operations Research and Enterprise Systems, ICORES 2012 - Vilamoura, Algarve, Portugal Duration: Feb 4 2012 → Feb 6 2012 |

### Other

Other | 1st International Conference on Operations Research and Enterprise Systems, ICORES 2012 |
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Country/Territory | Portugal |

City | Vilamoura, Algarve |

Period | 2/4/12 → 2/6/12 |

## Keywords

- Forward-Backward stochastic differential equations
- Optimal stochastic control
- Stochastic maximum principle

## ASJC Scopus subject areas

- Management Science and Operations Research