Particle Methods For Stochastic Optimal Control Problems

TL;DR

This paper introduces a variational approach with adaptive mesh discretization for solving stochastic optimal control problems, demonstrated through a hydro-electric dam management case study.

Contribution

It presents a novel variational framework and adaptive discretization method for stochastic control, addressing limitations of traditional dynamic programming and scenario tree approaches.

Findings

Effective solution algorithm for stochastic control problems

Application to hydro-electric dam management demonstrates practicality

Improved computational tractability over existing methods

Abstract

To tackle the difficulties faced by both stochastic dynamic programming and scenario tree methods, we present some variational approach for numerical solution of stochastic optimal control problems. We consider two different interpretations of the control problem, an algebraic and a functional one from which we derive optimality conditions. An adaptative mesh discretization method will be used to propose a tractable solution algorithm. An application to a hydro-electric dam production management problem will be presented.