2022-2023 FSU Mathematics Distinguished Lecture

Title: Recent computational methods for stochastic optimal control

Stochastic optimal control has been an effective tool for many problems in quantitative finance and financial economics. Although, they provide the much needed quantitative modeling for such problems, until recently they have been numerically intractable in high-dimensional settings. However, readily available and computationally highly effective optimization libraries now make regression type algorithms over hypothesis spaces with large number of parameters computationally feasible. In the context of stochastic optimal control, these exciting advances allow efficient approximations of the feedback controls. An algorithm, proposed by E, Jentzen & Han, uses deep artificial neural networks to approximate the feedback actions which are then trained by empirical risk minimization. This methodology and hybrid methods combined with dynamic programming have been explored and developed by many authors, including, Bachouch, Becker, Cheridito, Fecamp, Jentzen, Germain, Gonon, Hure, Langrene, Mikael, Pham, Teichmann, Warin, Welti, Wood. In this talk, I will outline this highly effective methodology and discuss it through representative examples from financial economics. This is based on joint works with Max Reppen of Boston University and Valentin Tissot-Daguette of Princeton University.