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Robust Markov Decision Processes and Applications in Mathematical Finance

Soori, Mohammad | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57559 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fotouhi Firouzabadi, Morteza; Salavati, Erfan
  7. Abstract:
  8. Dynamic portfolio optimization is one of the prominent problems in financial mathematics, for which numerous theories have been proposed to solve it. One of the solutions to this problem is the use of reinforcement learning. The main challenge with this method is that most reinforcement learning algorithms require a large amount of data, and therefore, the necessary data is often obtained not from the real world, but through simulations by estimating the parameters of a model. However, the approximation error of the parameters can propagate through the final solution, leading to inaccurate results. One approach to addressing this issue is the use of robust Markov processes and robust reinforcement learning. By relying on the robustness of these methods, it is possible to control the propagation of parameter errors in the final distribution, thereby reaching a reasonable solution. This thesis, after reviewing all the necessary theoretical concepts from the literature on reinforcement learning, stochastic calculus, and financial mathematics, and focusing on some recent research in robust Markov processes, addresses the problem of dynamic portfolio optimization using these processes. It relies on financial mathematics models for simulation and data generation, and analyzes and evaluates the obtained results
  9. Keywords:
  10. Robust Optimization ; Portfolio Optimization ; Markov Decision Making ; Reinforcement Learning ; Stochastic Calculations ; Markowitz Theory ; Heston Model ; BlackScholes Model ; Robust Reinforcement Learning

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