## Seminar Computational Finance Fall 2017

The goal of the seminar is to understand, implement and improve several novel techniques from machine learning in Finance. Concretely we shall teach a machine a calibration functional, i.e. how to map market data to appropriate models, or we teach a machine how to optimally hedge options given a pre-specified model for market prices, or how to solve non-linear PDEs, or how to filter signals from noisy observations possibly via rough paths methods. Prerequisities are some knowledge in mathematical Finance (pricing, hedging, optimal investment) and in Stochastic analysis, some understanding of neural networks, universal approximation theorems and network traning and some knowledge in implementation of machine-learning algorithms in Python. I recommend the following reading list and in particular the references on universal approximation in the first paper:

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The first meeting for the seminar is on Wednesday, September 20, in my office in G floor at 4 pm.

- Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen: Optimal Approximation with Sparsely Connected Deep Neural Networks, arxiv.1705.01714.
- Andres Hernandez: Model Calibration with neural networks, SSRN.2812140.
- Michael Kohler, Adam Krzyzak, Nebjosa Todorovic: Pricing of high-dimensional American Options by neural networks, Mathematical Finance 2010.
- Weinan E, Jiequn Han, Arnulf Jentzen: Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, arxiv.1706.04702.
- Christa Cuchiero, Josef Teichmann, et al: Bayesian Finance -- a machine learning approach to a simple calibration problem, slides, 2017.
- Terry Lyons, Rough paths, Signatures and the modelling of functions on streams, arxiv.1405.4537.