Lukas Gonon

Welcome to my personal homepage. I am an assistant professor at University of St. Gallen, affiliated with the School of Computer Science and the Center for Financial Services Innovation. I am also a Honorary Senior Lecturer at Imperial College London, where I previously held a Senior Lecturer (assistant professor) position.

Prior to that I obtained my doctoral degree from ETH Zürich, was a postdoctoral researcher at University of St. Gallen and an assistant professor at University of Munich.

My research focuses on foundations and applications of artificial intelligence, particularly in finance. It centers around various machine learning methods (deep learning, reservoir computing, random features, kernel methods, ...) and their applications to time series, stochastic processes, partial differential equations and finance. This encompasses

• applying and refining these methods or developing novel methods for practically important applications (for example hedging, forecasting or financial bubble detection)
• developing foundations for these methods (for instance providing guarantees on the approximation or generalization errors of deep or recurrent neural networks) in order to make them more accessible.

Email  /  Google Scholar  /  Homepage at University of St. Gallen

• Deep Learning (MATH70116) for the MSc in Mathematics and Finance

• Efficient Trading with Price Impact with X. Brokmann, G. He, D. Itkin, J. Muhle-Karbe
  Preprint, 2024 [ SSRN]
• Computing Systemic Risk Measures with Graph Neural Networks with T. Meyer-Brandis, N. Weber
  Preprint, arXiv:2410.07222 [arXiv]
• An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning with A. Jentzen, B. Kuckuck, S. Liang, A. Riekert, P. von Wurstemberger
  Preprint, arXiv:2408.13222 [arXiv]
• Variance Norms for Kernelized Anomaly Detection with T. Cass, N. Zozoulenko
  Preprint, arXiv:2407.11873 [arXiv]
• Operator Deep Smoothing for Implied Volatility with A. Jacquier, R. Wiedemann
  Preprint, arXiv:2406.11520 [arXiv]
• Universal randomised signatures for generative time series modelling with F. Biagini, N. Walter
  Preprint, arXiv:2406.10214 [arXiv]
• Universal approximation theorem and error bounds for quantum neural networks and quantum reservoirs with A. Jacquier
  Preprint, arXiv:2307.12904 [arXiv]
• The necessity of depth for artificial neural networks to approximate certain classes of smooth and bounded functions without the curse of dimensionality with R. Graeber, A. Jentzen
  Preprint, arXiv:2301.08284 [arXiv]
• Reservoir kernels and Volterra series with L. Grigoryeva, J.-P. Ortega
  Preprint, arXiv:2212.14641 [arXiv]
• Weak error analysis for stochastic gradient descent optimization algorithms with A. Bercher, A. Jentzen, D. Salimova
  Preprint, arXiv:2007.02723 [arXiv]

• Fast Deep Hedging with Second-Order Optimization with A. Akkari, K. Müller, B. Wood
  ICAIF '24: Proceedings of the 5th ACM International Conference on AI in Finance, 2024 [Article | arXiv]
• Detecting asset price bubbles using deep learning with F. Biagini, A. Mazzon, T. Meyer-Brandis
  Mathematical Finance, 2024 [Article | arXiv]
• Infinite-dimensional reservoir computing with L. Grigoryeva, J.-P. Ortega
  Neural Networks, 2024 [Article | arXiv]
• Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models with F. Biagini, N. Walter
  SIAM Journal on Financial Mathematics, 2024 [Article | arXiv]
• Deep neural network expressivity for optimal stopping problems
  Finance and Stochastics, 2024. [Article | arXiv]
• Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
  with C. Beck, A. Jentzen
  Partial Differential Equations and Applications, 2024. [Article |arXiv]
• Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality
  Journal of Machine Learning Research, 24(189), 1−51, 2023. [Article | arXiv]
• Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations with C. Schwab
  Analysis and Applications, 2023. [Article | arXiv]
• Neural network approximation for superhedging prices with F. Biagini, T. Reitsam
  Mathematical Finance, 33(1), 146-184, 2023. [Article | arXiv]
• Approximation Bounds for Random Neural Networks and Reservoir Systems with L. Grigoryeva, J.-P. Ortega
  Annals of Applied Probability, 33(1), 28-69, 2023. [Article |arXiv]
• Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models with C. Schwab
  Finance and Stochastics, 25, 615–657, 2021. [Article | arXiv]
• Discrete-time signatures and randomness in reservoir computing with C. Cuchiero, L. Grigoryeva, J.-P. Ortega, J. Teichmann
  IEEE Transactions on Neural Networks and Learning Systems, 2022, 33(11):6321-6330. [Article | arXiv]
• Expressive power of randomized signature with C. Cuchiero, L. Grigoryeva, J.-P. Ortega, J. Teichmann
  NeurIPS 2021 Workshop on The Symbiosis of Deep Learning and Differential Equations, 2021. [Article]
• Fading memory echo state networks are universal with J.-P. Ortega
  Neural Networks, 138, 10-13, 2021. [Article | arXiv]
• Asset Pricing with General Transaction Costs: Theory and Numerics with J. Muhle-Karbe, X. Shi
  Mathematical Finance, 31(2), 595–648, 2021. [Article | arXiv | Code]
• Uniform error estimates for artificial neural network approximations for heat equations with P. Grohs, A. Jentzen, D. Kofler, D. Siska
  IMA Journal of Numerical Analysis, 42(3), 1991-2054, 2022. [Article |arXiv]
• Risk bounds for reservoir computing with L. Grigoryeva, J.-P. Ortega
  Journal of Machine Learning Research, 21(240), 1-61, 2020. [Article |arXiv]
• Memory and forecasting capacities of nonlinear recurrent networks with L. Grigoryeva, J.-P. Ortega
  Physica D, 414, 132721, 1-13, 2020. [Article |arXiv]
• Reservoir Computing Universality With Stochastic Inputs with J.-P. Ortega
  IEEE Transactions on Neural Networks and Learning Systems, 2020. [Article | arXiv]
• Deep Hedging with H. Bühler, J. Teichmann, B. Wood
  Quantitative Finance, 2019. [Article | SSRN | arXiv]
  Media coverage: Risk Magazine
• Deep hedging: hedging derivatives under generic market frictions using reinforcement learning with H. Bühler, J. Teichmann, B. Wood
  NIPS 2018 Workshop on Challenges and Opportunities for AI in Financial Services, 2018 [Article]
  
• Linearized Filtering of Affine Processes Using Stochastic Riccati Equations with J. Teichmann
  Stochastic Processes and their Applications, 2020. [Journal version | arXiv]
• Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations
  with L. Döring, D. Prömel, O. Reichmann
  Journal of Theoretical Probability, 34, 173-205, 2021. [Article | arXiv]
• On existence and uniqueness properties for solutions of stochastic fixed point equations with C. Beck, M. Hutzenthaler, A. Jentzen
  Discrete & Continuous Dynamical Systems - B, 26(9), 4927-4962, 2021. [Article| arXiv]
• On Skorokhod Embeddings and Poisson Equations with L. Döring, D. Prömel, O. Reichmann
  Annals of Applied Probability, 2019. [Article | arXiv]
• Evolution of Firm Size with L.C.G. Rogers
  International Journal of Theoretical and Applied Finance, 2014. [Article]
• Online Model Estimation of Ultra-Wideband TDOA Measurements for Mobile Robot Localization with A. Prorok, A. Martinoli
  IEEE International Conference on Robotics and Automation (ICRA), pp. 807-814, 2012. [Article]