The randomization method in stochastic optimal control

2025/02/10 by Marco Fuhrman, Fuhrman, Marco · 1 citation
Earth and Planetary Sciences · #Aquatic and Environmental Studies

paper · pdf · doi:10.48550/arxiv.2502.06356

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.

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