Summary
Lukas is a Senior Lecturer jointly appointed at the Department of Mathematics and the artificial intelligence initiative Imperial-X (I-X).
Lukas holds a doctoral degree from ETH Zürich and has been a postdoctoral researcher at University of St. Gallen and an assistant professor at University of Munich before joining Imperial College London.
His research is at the intersection of mathematics, machine learning and finance. It centers around various machine learning methods (deep learning, reservoir computing, random features, kernel methods, ...) and their applications to stochastic processes, partial differential equations and mathematical finance. This encompasses
(i) applying and refining these methods or developing novel methods for practically important applications (for example hedging or financial bubble detection)
(ii) carrying out mathematical analyses (for instance proving bounds on the approximation or generalization errors of deep or recurrent neural networks for pricing or learning stochastic processes) in order to gain a more profound theoretical understanding of these methods.
Lukas serves as an action editor for Neural Networks.
For a full list of publications and preprints see Lukas' personal homepage or his google scholar profile.
Selected Publications
Journal Articles
Gonon L, Grigoryeva L, Ortega JP, 2023, APPROXIMATION BOUNDS FOR RANDOM NEURAL NETWORKS AND RESERVOIR SYSTEMS, Annals of Applied Probability, Vol:33, ISSN:1050-5164, Pages:28-69
Biagini F, Gonon L, Reitsam T, 2023, Neural network approximation for superhedging prices, Mathematical Finance, Vol:33, ISSN:0960-1627, Pages:146-184
Gonon L, 2023, Random feature neural networks learn Black-Scholes type PDES without curse of dimensionality, Journal of Machine Learning Research, Vol:24, ISSN:1532-4435, Pages:1-51
Gonon L, Schwab C, 2021, Deep ReLU network expression rates for option prices in high-dimensional, exponential Levy models, Finance and Stochastics, Vol:25, ISSN:0949-2984, Pages:615-657
Cuchiero C, Gonon L, Grigoryeva L, et al., 2021, Discrete-Time Signatures and Randomness in Reservoir Computing, IEEE Transaction on Neural Networks and Learning Systems, Vol:33, ISSN:2162-237X, Pages:6321-6330
Gonon L, Grigoryeva L, Ortega J-P, 2020, Risk Bounds for Reservoir Computing, Journal of Machine Learning Research, Vol:21, ISSN:1532-4435
Buehler H, Gonon L, Teichmann J, et al., 2019, Deep hedging, Quantitative Finance, Vol:19, ISSN:1469-7688, Pages:1271-1291