Robust and Stable Deep Learning Algorithms for Forward Backward Stochastic Differential Equations скачать в хорошем качестве

Robust and Stable Deep Learning Algorithms for Forward Backward Stochastic Differential Equations

Timestamps 0:00 - Intro 2:39 - Partial Differential Equations 3:43 - Stochastic Differential Equations 6:08 - Brownian Motion 8:06 - Non-linear PDEs 8:52 - Designing a Neural Network 12:28 - Black-Scholes example 13:47 - Stability and Generalisation 15:45 - Computational Efficiency 18:25 - Conclusion 20:08 - Q&A Data Science Meetup of the Analytics Club at ETH Zurich Speaker: Alexis Laignelet (PhD Student at Imperial College London) Publication: https://arxiv.org/abs/1910.11623 Presentation and more: https://github.com/alaignelet/alaigne... Sign up for our newsletter or become a member of the Analytics Club (for students in Switzerland): https://analytics-club.org If you are interested in getting involved with a board position at the Analytics Club to organise events like this one, please fill out the form below or reach out to us for more information through info@analytics-club.org ACE board form: https://forms.gle/jmTxeur8JK9KtcJZA Paper Abstract: Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection between PDEs and systems of Forward-Backward Stochastic Differential Equations (FBSDEs) enables the use of advanced simulation techniques to be applied even in the high dimensional setting. Unfortunately, when the underlying application contains nonlinear terms, then classical methods both for simulation and numerical methods for PDEs suffer from the curse of dimensionality. Inspired by the success of deep learning, several researchers have recently proposed to address the solution of FBSDEs using deep learning. We discuss the dynamical systems point of view of deep learning and compare several architectures in terms of stability, generalization, and robustness. In order to speed up the computations, we propose to use a multilevel discretization technique. Our preliminary results suggest that the multilevel discretization method improves solutions times by an order of magnitude compared to existing methods without sacrificing stability or robustness.