Lukasz Szpruch

University of Edinburgh

I'm a Professor at the School of Mathematics, the University of Edinburgh, and the Programme Director for Finance and Economics at the The Alan Turing Institute, the National Institute for Data Science and AI. At Turing, I'm providing academic leadership for partnerships with the National Office for Statistics, Accenture, Bill and Melinda Gates Foundation and HSBC. I'm the Principle Investigator of the research programme FAIR on responsible adoption of AI in the financial services industry. I'm also a co-Investigator of the UK Centre for Greening Finance & Investment (CGFI). I'm also an affiliated member of the Oxford-Man Institute for Quantitative Finance.

Before joining Edinburgh, I was a Nomura Junior Research Fellow at the Institute of Mathematics, University of Oxford.

Research Topic

My broad research interests span probability theory, stochastic analysis and theoretical machine learning. I am currently researching on the mathematical foundation of deep learning, mean-field models, (inverse) reinforcement learning, game theory and multiagent sysmtems, sampling and optimisation algorithms, computational optimal transport, and the theory of gradient flows. I'm also interested in applications of these areas in finance and economics.

For updates on my research see my Google Scholar page. You may also check my profile on the Research Gate or the MathSciNet

  • Cao, H., Cohen, S. and Szpruch, L., 2021. Identifiability in inverse reinforcement learning. Advances in Neural Information Processing Systems, 34, pp.12362-12373. NeurIPS Proceedings
  • Kerimkulov, B., Siska, D. and Szpruch, L., 2021. A modified MSA for stochastic control problems. Applied Mathematics & Optimization, 84(3), pp.3417-3436. arXiv
  • Ni, H., Szpruch, L., Sabate-Vidales, M., Xiao, B., Wiese, M. and Liao, S., 2021, November. Sig-Wasserstein GANs for time series generation. In Proceedings of the Second ACM International Conference on AI in Finance (pp. 1-8).arXiv
  • Sabate Vidales, M., SiSka, D. and Szpruch, L., 2021. Unbiased Deep Solvers for Linear Parametric PDEs. Applied Mathematical Finance, pp.1-31.arXiv
  • Cohen, S.N., Snow, D. and Szpruch, L., 2021. Black-box model risk in finance. book chapter in Machine Learning And Data Sciences For Financial Markets: A Guide To Contemporary Practices, Cambridge University Press 2022. arXiv
  • Arribas I.P., Salvi C., Szpruch L., Sig-SDEs model for quantitative finance, proceedings of ICAIF 2020. arXiv
  • Duncan A., Nusken N., Szpruch L., On the geometry of Stein variational gradient descent, JMLR, 2021 arXiv
  • Kaitong H., Zhenjie R., Siska., Szpruch L., Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks, Ann. Inst. H. Poincaré Probab. Statist., 2021 arXiv
  • Szpruch L., Tse A., Antithetic multilevel particle system sampling method for McKean-Vlasov SDEs, The Annals of Applied Probability 31.3 (2021): 1100-1139. arXiv
  • Chassagneux JF., Szpruch L., Tse A., Weak quantitative propagation of chaos via differential calculus on the space of measures, The Annals of Applied Probability, 32(3), pp.1929-1969., 2022 arXiv
  • Hammersley R. P. W, Siska D., Szpruch L., McKean-Vlasov SDEs under Measure Dependent Lyapunov Conditions, Ann. Inst. H. Poincaré Probab. Statist., 57(2), 1032-1057, 2021 journal, arXiv
  • Kerimkulov B., Siska D., Szpruch L., A modified MSA for stochastic control problems, Applied Mathematics & Optimization, 2021 journal, arXiv
  • Hammersley R. P. W, Siska D., Szpruch L., Weak Existence and Uniqueness for McKean-Vlasov SDEs with Common Noise, Annals of Probability, 49(2), 527-555, 2021 arXiv
  • Kerimkulov B., Siska D., Szpruch L., Exponential Convergence and stability of Howards's Policy Improvement Algorithm for Controlled Diffusions, SIAM J. Control Optim., 58(3), 1314–1340. journal,arXiv
  • Majka M.B., Mijatovic A., Szpruch L, Non-asymptotic bounds for sampling algorithms without log-concavity, to appear in Annals of Applied Probability, arXiv
  • Giles M.B., B. Majka M.B., Szpruch L, Vollmer S., Zygalakis K., Multilevel Monte Carlo methods for the approximation of invariant measures of stochastic differential equations, Statistics and Computing, 2019 arXiv
  • Szpruch L., Tan S., Tse A., Iterative Particle Approximation for McKean-Vlasov SDEs with application to Multilevel Monte Carlo estimation, Annals of Applied Probability Volume 29, Number 4 (2019), 2230-2265. journal, arXiv
  • Neuenkirch A., Szolgyenyi M, Szpruch L., An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis, SIAM J. Numer. Anal. 57-1 (2019), pp. 378-403. journal, arXiv
  • AlRachid H., Bossy M., Ricci C., Szpruch L., New particle representations for ergodic McKean-Vlasov SDEs, ESAIM: ProcS Volume 65, 2019 journal, arXiv
  • Szpruch, L. Zhang, X. V-Integrability, Asymptotic Stability And Comparison Theorem of Explicit Numerical Schemes for SDEs, Mathematics of Computations 87 (2018), 755-783 , arXiv
  • Lionnet A., dos Reis G. and Szpruch L., Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth , Annals of Applied Probability. Volume 28, Number 4 (2018), 2544-2591., journal arXiv
  • Lionnet, A., dos Reis, G and Szpruch, L., Time discretisation of FBSDE with polynomial growth drivers and reaction-diffusion PDEs, Annals of Applied Probability, Vol. 25, 2563-2625, Number 5, 2015. arXiv
  • Giles, M.B. and Szpruch, L., Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without L\'{e}vy area simulation, Annals of Applied Probability, Vol. 24, 1585-1620 , Number 4 2014. arXiv
  • Neuenkirch, A. and Szpruch, L., First order strong approximations of scalar SDEs with values in a domain, Numerische Mathematik, Vol. 128-1, pp 103-136, 2014. arXiv
  • Higham, D.J., Mao, X. and Szpruch, L. Convergence, non-negativity and stability of a new Milstein Scheme with applications to finance, DCDS-B,18(8):2083 - 2100, AIMS, 2013 arXiv
  • Giles, M.B. and Szpruch, L, Antithetic multilevel Monte Carlo estimation of financial options in Monte Carlo and Quasi-Monte Carlo Methods 2012. arXiv
  • Cohen, S.N. and Szpruch, L. On Markovian Solutions to Markov Chain BSDEs Numerical Algebra, Control and Optimization, 2012, 2(2):257-269 arXiv
  • Cohen, S.N. and Szpruch, L. A limit order book model for latency arbitrage, Mathematics and Financial Economics, 6(3):211-227, 2012. arXiv
  • Dereich, S., Neuenkirch, A. and Szpruch, L., An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process, Proceedings of the Royal Society A, Vol. 468, No. 2140, pp. 1105–1115, 2012. arXiv
  • Mao X., and Szpruch L., Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients, Journal of Computational and Applied Mathematics, 238:14-28,2013 arXiv
  • Szpruch, L. and Mao. X., Strong convergence rates for backward Euler-Maruyama method for dissipative-type stochastic differential equations with super-linear diffusion coefficients, Stochastics, 85, no. 1, 144171, 2013. preprint
  • Higham, D. J. , Intep, S., Mao, X., and Szpruch, L., Hybrid Simulation of auto-regulation within transcription and translation, BIT Numer Math., Vol. 51, No. 1, pp. 177-196, 2011.
  • Szpruch, L. Mao X., Higham, D. J., and Pan, J., Numerical simulation of a strongly nonlinear Ait- Sahalia-type interest rate model, BIT Numer Math, Vol. 51, No. 2, pp. 405-425, 2011.
  • Wu, F., Mao, X. and Szpruch L., Almost sure exponential stability of numerical solutions for stochastic delay differential equations, Numerische Mathematik, Vol. 115, No. 4, pp. 681-697, 2010.
  • Szpruch, L., Higham, D. J., Comparing hitting time behavior of Markov jump processes and their diffusion approximations, Multiscale Model. Simul., No. 8, pp. 605-621, 2010.
    S. Cohen, I. Gyöngy, G. dos Reis, D. Siska and L. Szpruch (eds.), Frontiers in Stochastic Analysis – BSDEs, SPDEs and their Applications, Springer, 2019 book
  • Giles, M.B. and Szpruch, L, Multilevel Monte Carlo methods for applications in finance, in: Gerstner, Kloeden (Eds.), Recent Advances in Computational Finance, World Scientific, 2013. arXiv
Current Research Group
Past members of the group

Lukasz Szpruch
The University of Edinburgh
James Clerk Maxwell Building
Peter Guthrie Tait Road
Edinburgh EH9 3FD

E-mail: l.szpruch[at]