I am a Reader (Associate Professor) at the School of Mathematics, University of Edinburgh. I am also a Research Fellow at the Alan Turing Institute, London. Before moving to Edinburgh, I was a Nomura Junior Research Fellow at the Institute of Mathematics, University of Oxford, and a member of the Oxford-Man Institute for Quantitative Finance. I hold a Ph.D. in Mathematics from the University of Strathclyde in Glasgow.

My research interests focus on probability theory and its applications.

I am currently researching on: Stochastic McKean-Vlasov Equations, Mean Field models, Stochastic Interacting Particle systems, Forward-Backward Stochastic Differential Equations, Markov Chain Monte Carlo methods and Multilevel Monte Carlo methods

At the Turing Insitute, I co-organise the interest group Sampling algorithms for data analytics

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

- Szpruch L., Tan S., Tse A., Iterative Particle Approximation for McKean-Vlasov SDEs with application to Multilevel Monte Carlo estimation,
*arXiv* - Lionnet A., dos Reis G. and Szpruch L., Full-Projection scheme for monotone BSDEs with polynomial growth,
*arXiv* - Lionnet A., dos Reis G. and Szpruch L., Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth
, to appear in Annals of Applied Probability,
*arXiv* - Mike Giles, Tigran Nagapetyan, Lukasz Szpruch, Sebastian Vollmer, Konstantinos Zygalakis, Multilevel Monte Carlo for Scalable Bayesian Computations
*arXiv* - Szpruch, L. Zhang, X. V-Integrability, Asymptotic Stability And Comparison Theorem of Explicit Numerical Schemes for SDEs,
to appear in Mathematics of Computations, AMS,
*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.

- 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*

- Shuren Tan - PhD student (2015-now)
- Alvin Tse - PhD student (2016-now)
- William Hammersley - PhD student (2017-now)

Lukasz Szpruch

The University of Edinburgh

James Clerk Maxwell Building

Peter Guthrie Tait Road

Edinburgh EH9 3FD

E-mail: l.szpruch[at]ed.ac.uk