Lecturers: |
J.D. Fermanian and H. Pham |

Period: |
Term 3 |

ECTS: |
6 |

Schedule: |
3 hours per week |

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.

**Part I: Fundamental concepts from machine learning**

1. Presentation of the main machine learning algorithms

2. Overlearning: penalization, regularization, cross-validation

3. Presentation of the main scoring techniques

4. Deep learning: Multi-layer feedforward neural networks, convolutional, recurrent networks. Backpropagation, stochastic gradient for training. Implementation with TensorFlow

**Part II: Applications in finance**

1. Text data processing and stock market prediction

2. Deep hedging and deep calibration

3. Deep reinforcement learning and applications

- Q-learning algorithms, policy gradient, actor-critic algorithm

- Stochastic control and portfolio optimisation

- Nonlinear PDE, American option pricing, counterparty risk (CVA).

4. Market generators and deep simulation

**References**

[1] A. Bachouch, C. Huré, N. Langrené, H. Pham : Deep neural networks algorithms for stochastic control problems on finite horizon, part II, numerical applications : to appear in Methodology and Computing in Applied Probability.

[2] C. Bayer, B. Horvath, A. Muguruza, B. Stemper, M. Tomas : On deep calibration of (rough) stochastic volatility models, arXiv : 1908.08806

[3] D. Bloch : Machine learning : models and algorithms, {\it Quantitative Analytics}, 2020.

[4] H. Buehler, L. Gonon, J. Teichmann, B. Wood : Deep hedging, {\it Quantitative Finance}, 19(8), 1271-1291, 2019.

[5] S. Eckstein and M. Kupper : Computation of optimal transport and related hedging problems via penalization and neural networks. Applied Mathematics and Optimization, 1-29, 2019.

[6] C. Huré, H. Pham, X. Warin : Deep backward schemes for high-dimensional nonlinear PDEs, Mathematics of Computation. 2019

[7] P. Henry-Labordère : Generative models for financial data, SSRN 3408007, 2019

[8] M. Lopez de Prado : Advances in machine learning, Wiley, 2016.