Machine Learning Techniques Applied to Robust Optimal Control Problems

Faculty-development competitive research grants program for 2023-2025

This project aims at making several contributions to develop and analyze robust methods in financial mathematics and robust stochastic control problems in general. The main research efforts will focus on the settings, where there is uncertainty in the dynamics of the stochastic processes representing different components of the financial instruments such as current price of an option written on a stock. Furthermore, we will examine our theoretical results with numerical studies to see the effects of our methodologies. Secondary objectives of the project are:
● Training MSc and PhD students at Nazarbayev University
● Representing Kazakhstan in international scientific meetings
● Involving Nazarbayev University students as research assistants.

The proposed research project is divided into three main scientific objectives:
O1. Finding optimal controls of problems on coherent risk measures and its numerics using machine learning (ML) techniques
O2. Studying optimal stopping problems with coherent risk measures and its numerics using ML techniques
O3. Finding optimal controls of problems on cumulative prospect theory using ML techniques

The proposed research project aims at making contributions to develop more realistic models in financial mathematics. The major output of this work will be a series of publications in journals of high reputation in the field of financial and applied mathematics that are science-indexed [37]. It is anticipated that the results obtained within the framework of this research project will contribute to the current state-of-the-art mathematical models in finance. In order to share the results of this research proposal and build further connections with the experts of the field, members of this project will attend internationally recognized conferences such as the approaching SIAM Conference on Financial Mathematics and Engineering [38] and Bachelier Finance Society 12nd World Congress [39]. Furthermore, most of the members of this project involve young researchers pursuing graduate studies. Thus, one of the essential impacts on the scientific community of Kazakhstan will be the training of these researchers.