Machine learning in finance: Theoretical foundations

Objectif

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, 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, market generators, deep reinforcement learning and trading portfolio.   

Plan

•  Part I.   Fundamental concepts from machine learning

1. Presentation of the main machine learning algorithms and specificities to financial time series
2. False discovery and back-testing 
3. Presentation of  scoring techniques 
4. Deep learning:  Multi-layer feedforward neural networks, LSTM Backpropagation, stochastic gradient for training Implementation with TensorFlow

• Part II. Applications in finance

1. Gaussian process regression and financial  applications
2. Deep optimization in finance: deep hedging, deep calibration, generative modeling and market generators
3. Neural networks-based algorithms for high-dimensional problems: 

• Stochastic control: policy and value function learning
• Non linear PDEs in finance (Deep Galerkin, Deep BSDE) 

     4. Deep reinforcement learning

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

Références

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