Research

Research interests

My research interests focus on mathematical aspects of machine learning, computational statistics and uncertainty quantification

  • Theoretical
    • Deep learning
    • Mathematical modeling
    • Numerical analysis
    • Statistical inverse problems
    • Uncertainty quantification
  •  Methodical
    • Monte Carlo and Markov chain Monte Carlo methods
    • Numerical discretization schemes for PDEs and SDEs
    • Automatic adjoint differentiation
    • Parallel computing on CPU (MPI and OpenMP) and GPU (CUDA)
  • Applications 
    • Deep learning pricing, hedging and calibration of financial models
    • Financial climate risk management
    • Statistical inference of model parameters from time series data

Monograph

Anomaly Detection in Random Heterogeneous Media, Springer Spektrum, Wiesbaden, 2015.

Publications

  1. (with P. Piiroinen and L. Roininen) Brexit risk implied by the SABR martingale defect in the EUR-GBP smile, Preprint (2019) arXiv:1912.05773
  2. (with P. Piiroinen, L. Roininen and T. Schoden) Asset price bubbles: An option-based indicator, Preprint (2018) arXiv:1805.07403
  3. (with P. Piiroinen) Probabilistic interpretation of the Calderón problem, Inverse Probl. Imaging, 11 (2017), 553-575
  4. (with P. Piiroinen) From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography, Ann. Appl. Probab., 26 (2016), 3001-3043
  5. (with S. Maire) A partially reflecting random walk on spheres algorithm for electrical impedance tomography, Journal of Computational Physics, 303 (2015), 413–430
  6. Bayesian anomaly detection in heterogeneous media with applications to geophysical tomography, Inverse Problems, 30 (2014), 114013
  7. (with P. Piiroinen) Probabilistic interpretation of electrical impedance tomography, Preprint (2014) arXiv:1403.2883
  8. (with N. Sfakianakis) Inverse modeling of the Drosophila gap gene system: sparsity promoting Bayesian parameter estimation and uncertainty quantification, Proceedings of the 10th International Workshop on Computational Systems Biology, WCSB 2013 (2013), 86–90
  9. (with M. Hanke and P. Piiroinen) Multilevel Bayesian reconstruction in impedance tomography, Oberwolfach Rep. 11 (2012), 617–619

Reviews

I served as peer reviewer for the following journals and conference proceedings:

  • Digital Signal Processing
  • Inverse Problems
  • Journal of Computational and Applied Mathematics
  • Mathematical Methods in the Applied Sciences
  • Proceedings of the International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Leuven, Belgium, 2014

Organization of conferences, symposia and workshops

Selected presentations

  • Financial climate risk management, BNP Paribas, Frankfurt am Main, Germany, 16 September 2021
  • Stock price bubbles: An option-based indicator, MathFinance Conference 2019, Frankfurt School of Finance & Management, Germany, 8 April 2019
  • Data-driven stock price bubble detection: A practitioners perspective, Workshop on SDEs with Applications in Finance, Lappeenranta University of Technology, Finland, 21 March 2019
  • Stock price bubbles: An option-based indicator, Analysis and Stochastics Seminar, Technische Universität Dresden, Germany, 29 November 2018
  • Aktienpreisblasen: Ein optionsbasierter Indikator, Seminar Angewandte Analysis und Numerik, Goethe-Universtät, Frankfurt am Main, Germany, 22 November 2018
  • Stock price bubbles: An option-based indicator, Finance and Stochastics Seminar, Imperial College, London, England, 14 November 2018
  • Statistical methods for pricing and risk management of coco-bonds, SIAM Conference on Uncertainty Quantification, Lausanne, Switzerland, 5 April 2016
  • Bayesian approach to the inverse problem of option pricing and detection of financial bubbles, Applied Inverse Problems Conference, Helsinki, Finland, 26 May 2015
  • Electrical impedance tomography with probabilistic forward models, International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Leuven, Belgium, 6 April 2014
  • Shape reconstruction in impedance tomography for highly heterogeneous background conductivity, International Conference on Inverse Problems and Related Topics, Southeast University, Nanjing, China, 26 October 2012
  • A Feynman-Kac-type formula for impedance tomography, SIAM Conference on Imaging Science, Philadelphia, Pennsylvania, USA, 21 May 2012
  • Multilevel Bayesian reconstruction in impedance tomography, Workshop on Inverse Problems for Partial Differential Equations, Mathematisches Forschungsinstitut Oberwolfach, Germany, 23 February 2012
  • Multilevel Bayesian reconstruction of heterogeneous microstructure, TOSCA Seminar, INRIA Sophia Antipolis Méditerrannée, France, 19 January 2012
  • Ein probabilistisches Verfahren für die Rekonstruktion heterogener Mikrostrukturen, Rhein Main Arbeitskreis Mathematics of Computation, Technical University Darmstadt, Germany, 3 February 2012
  • Multilevel MCMC reconstruction of heterogeneous microstructure, 17th Inverse Days of the Finnish Inverse Problems Society, University of Helsinki, Finland, 14 December 2011
  • Probabilistic interpretation of current-to-voltage-maps within the complete electrode model of EIT, Applied Inverse Problems Conference, College Station, Texas, USA, 23 May 2011