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

M. Germain,  H. Pham, X. Warin: Neural networks-based algorithms for stochastic control and PDEs in finance, Machine learning for finnacial markets, a guide to contemporary practices, Cambridge University Press 
C. Bayer, B. Horvath, A. Muguruza, B. Stemper, M. Tomas : On deep calibration of (rough) stochastic volatility models, arXiv : 1908.08806
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.
I. Goodfellow, Y. Bengio, A. Courville : Deep learning, 2016.
P. Henry-Labordère : Generative models for financial data, SSRN 3408007, 2019
M. Lopez de Prado : Advances in machine learning, Wiley, 2016.
R. Sutton, A. Barto : Reinforcement Learning, An Introduction, 2018, 2nd edition