Machine learning in finance: Theoretical foundations

Objective

The aim of this lecture is to introduce some fundamental concepts and techniques from machine learning and deep learning with a view towards important and recent applications in finance : This includes advanced techniques in scoring, text mining for stock market prediction, hedging/pricing of options, calibration of models, optimal transport and robust finance, numerical resolution of high-dimensional non-linear partial differential equations arising for instance in stochastic control and portfolio selection, market generators.

Planning

Part I: Fundamental concepts from machine learning (9h)

• Presentation of the main machine learning algorithms
• Overlearning: penalization, regularization, cross-validation
• Presentation of the main scoring techniques
• Deep learning
  • Multi-layer feedforward neural networks, convolutional, recurrent networks.
  • Backpropagation, stochastic gradient for training.
  • Implementation with TensorFlow

Part II: Applications in finance (15h)

• Text data processing and stock market prediction (3h)
• Deep hedging and deep calibration (3h)
• Deep reinforcement learning and applications (6h)
  • Q-learning algorithms, policy gradient, actor-critic algorithm
  • Stochastic control and portfolio optimization
  • Nonlinear PDE, American option pricing, counterparty risk (CVA).

4. Market generators and deep simulation (3h)

References

•  A. Bachouch, C. Huré, N. Langrené, H. Pham : Deep neural networks algorithms for stochastic control problems on finite horizon, part II, numerical applications : Methodology and Computing in Applied Probability. 
•  D. Bloch : Machine learning : models and algorithms, Quantitative Analytics, 2020. 
•  H. Buehler, L. Gonon, J. Teichmann, B. Wood : Deep hedging, Quantitative Finance, 19(8), 1271-1291, 2019. 
•  C. Huré, H. Pham, X. Warin : Deep backward schemes for high-dimensional nonlinear PDEs, Mathematics of Computation. 2020
• M. Hamdouche, P. Henry Labordère, H.Pham: Generative modeling for time series via Schrödinger bridge, 2023
•  M. Lopez de Prado :  Advances in machine learning, Wiley, 2016. 
• M. Germain, H. Pham, X. Warin: Neural networks-based algorithms for stochastic control and PDEs in finance, Machine Learning and Data Sciences for Financial Markets: a guide to contemporary practices, Cambridge University Press,  2023,  Editors: Agostino Capponi and Charles-Albert Lehalle
• M. Dixon, I. Halperin, P. Bilokon: Machine learning in Finance, 2020, Springer.