### Abstract

Deep learning algorithms have been shown empirically to work well in many classical problems from mathematical finance. Theoretical foundations of deep learning in this context, however, are far less developed. In this talk we present some recent results in this direction.

More specifically, the talk starts with examples of recent applications of deep learning to option pricing. Next, we discuss theoretical foundations of such methods, recent mathematical progress, and key challenges. Finally, we show that in certain situations random neural networks are capable of overcoming these challenges.

### Our speaker

Lukas Gonon is a Senior Lecturer at the Department of Mathematics at Imperial College London. His research is at the intersection of mathematics, machine learning and finance. The focus lies on various machine learning methods (deep learning, reservoir computing, random features, ...) and their applications to stochastic processes, partial differential equations and mathematical finance.

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