Lukasz Szpruch

University of Edinburgh

Introduction

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.

Research Topic

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

Preprints
Publications
  • 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.
Book Chapters
  • 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
Research Team
Contact

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