Stohastični kontrolni sistemi z uporabo strojnega učenja

Stochastic optimal control is a branch of applied mathematics concerned with optimising decisions in systems influenced by randomness. It plays an important role in various fields, including finance, energy markets, and engineering. Classical approaches to stochastic control have led to the development of both rich theoretical foundations and a range of numerical methods. In recent years, machine learning techniques have emerged as a powerful alternative for solving stochastic control problems, offering flexible and general approaches. This thesis investigates several stochastic control problems from both theoretical and computational perspectives. We begin by analysing the control of conditional McKean-Vlasov stochastic differential equations and the problem of optimal quadratic hedging, with particular attention to models involving jump processes. We also examine dynamic risk measures through their formulations using backward stochastic differential equations, a framework deeply connected to stochastic control theory. Furthermore, we study contracts in energy markets in the setting of Dynkin games, which we relate to doubly reflected backward stochastic differential equations. For each of these problems, we propose dedicated deep learning algorithms designed to provide effective numerical solutions. The performance of these methods is evaluated on benchmark examples. In the case of backward stochastic differential equations-based problems, the additional mathematical structure allows us to provide results on the convergence of the algorithms.