Optimal Control Strategies for Stochastic Differential Equations: A Computational Approach

Abstract

Optimal control strategies play a crucial role in various fields, including finance, engineering, and biology, where decision-making processes are subject to uncertainty and randomness. In this paper, we present a computational approach to address optimal control problems for stochastic differential equations (SDEs). We begin by introducing the fundamental concepts of SDEs and optimal control theory, highlighting the challenges posed by the inherent randomness and nonlinearity of SDEs. We then propose a computational framework for solving optimal control problems for SDEs, leveraging numerical methods such as stochastic optimization, Monte Carlo simulation, and dynamic programming. By discretizing the SDEs and formulating the control problem as a stochastic optimization problem, we develop algorithms to compute optimal control strategies that minimize or maximize the expected value of a given objective function subject to stochastic constraints.