Lukas Gonon

Welcome to my personal homepage. I am a senior lecturer at Imperial College London - Department of Mathematics and Imperial-X.

Previously, 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 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 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)
  • carrying out mathematical analyses (for instance proving bounds on the approximation or generalization errors of deep or recurrent neural networks) in order to gain a more profound theoretical understanding of these methods.

Email  /  Google Scholar  /  Homepage at Imperial

Lukas Gonon
Current Teaching at Imperial
Preprints

  • Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models with F. Biagini, N. Walter
    Preprint, arXiv:2309.14784 [arXiv]
  • Universal approximation theorem and error bounds for quantum neural networks and quantum reservoirs with A. Jacquier
    Preprint, arXiv:2307.12904 [arXiv]
  • Infinite-dimensional reservoir computing with L. Grigoryeva, J.-P. Ortega
    Preprint, arXiv:2304.00490 [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]
  • Detecting asset price bubbles using deep learning with F. Biagini, A. Mazzon, T. Meyer-Brandis
    Preprint, arXiv:2210.01726 [arXiv]
  • Weak error analysis for stochastic gradient descent optimization algorithms with A. Bercher, A. Jentzen, D. Salimova
    Preprint, arXiv:2007.02723 [arXiv]
Publications

Journals

  • Deep neural network expressivity for optimal stopping problems
    To appear in Finance and Stochastics, 2024. [arXiv]
  • Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
    with C. Beck, A. Jentzen
    To appear in Partial Differential Equations and Applications, 2024. [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]
  • 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
  • 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]
Conferences

  • 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]
  • 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]
  • 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]



Last modification: Feburary 2nd, 2024