English

The randomization method in stochastic optimal control

Optimization and Control 2025-06-12 v2 Probability

Abstract

In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic differential equation (BSDE), by means of an auxiliary optimization problem having the same value as the starting one. This method works for a large class of control problems and provides a BSDE representation to many related PDEs of Hamilton-Jacobi-Bellman type, even in the fully non linear case. After a general informal introduction we explain the method giving full details in a basic case. Then we try to give a complete picture of the existing applications and we present some related open problems.

Keywords

Cite

@article{arxiv.2502.06356,
  title  = {The randomization method in stochastic optimal control},
  author = {Marco Fuhrman},
  journal= {arXiv preprint arXiv:2502.06356},
  year   = {2025}
}

Comments

arXiv admin note: text overlap with arXiv:1511.09274