Machine learning in finance: Theoretical foundations

Objectif

The aim of this lecture is to: 

• introduce some fundamental concepts and modern techniques from machine learning and deep learning, with 
• a view towards important and recent applications in finance : this includes advanced techniques in scoring, hedging/pricing of options, calibration of models,  deep portfolio optimization,  numerical resolution of high-dimensional non-linear partial differential equations arising for instance in stochastic control and portfolio selection, generative modeling, deep reinforcement learning and trading portfolio.   

Plan

Part I on Wednesday feb. 5, 12, 19,  2025: 9h-10h30, 10h45-12h15
by Jean-David Fermanian

Fundamental concepts from machine learning

1. Presentation of the main machine learning algorithms and specificities to financial time series
2. Overlearning: penalization, regularization, cross-validation
3. False discovery and back-testing 
4. Presentation of  scoring techniques 
5. Deep learning 

• Multi-layer feedforward neural networks, LSTM 
•  Backpropagation, stochastic gradient for training  
• Implementation with  TensorFlow  

Part II on Wednesday march 5, 12, 29, 26, 2025: 9h-10h30, 10h45-12h15
by Huyên Pham 

Foundations and applications in finance

1. Gaussian process and financial applications
2.  Neural networks-based algorithms for high-dimensional problems 

• Deep hedging
•  Stochastic control: policy and value function learning
•  Non linear PDEs in finance: Deep Galerkin, Deep BSDE, Deep backward dynamic programming

      3. Deep  reinforcement learning and applications 

•  Q-learning algorithms, Deep Q-learning 
•  Policy gradient methods, actor-critic algorithms  
•   Some applications in finance:  optimal trading, market making

      4.  Generative modeling and markets generators 

•  GANs
• Diffusion models and Schrödinger bridge

Références

•  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.