Bertram is a research visitor at the Department of Applied Mathematics and Theoretical Physics as part of the Numerical Analysis group. His research interests are applied and computational partial differential equations, including modelling, analysis, numerical analysis and optimal control, with a particular interest in applications from finance and socio-economics.
Career
| 07/2020– | Professor of Mathematics, Mathematics Institute, University of Warwick, UK |
| 11/2018– | Research visitor, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK |
| 05/2018–07/2020 | Professor of Mathematics, Department of Mathematics, University of Sussex, UK |
| 09/2010–04/2018 | Senior Lecturer, then Reader in Mathematics, Department of Mathematics, University of Sussex, UK |
| 05/2007–08/2010 | Postdoctoral Research Fellow, then Privatdozent, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria |
| 11/2002–04/2007 | Research associate, then Postdoctoral Research Fellow, Institute for Mathematics at Johannes Gutenberg University Mainz, Germany |
| 11/1999–10/2002 | Research associate, Department of Mathematics and Statistics, University of Konstanz, Germany |
| 08/1998–09/1998 | Student internship, Systemtechnik und Software GmbH, Berlin, Germany |
Education
| 07/2010 | Habilitation (venia docendi) in Applied Mathematics, Vienna University of Technology, Austria |
| 10/2005 | Ph.D. (Dr. rer. nat.) in Mathematics, Johannes Gutenberg University Mainz, Germany |
| 10/1999 | Diplom (Dipl.-math. techn.) in Applied Mathematics, distinction, Technical University Berlin, Germany |
Publications
- B. Düring, J. Evans and M.-T. Wolfram. Steady states of an Elo-type rating model for players of varying strength. Kinet. Relat. Models, 2023. (arXiv:2204.10260)
- B. Düring and C. Heuer. Time-adaptive high-order compact finite difference schemes for option pricing in a family of stochastic volatility models. In: Progress in Industrial Mathematics at ECMI 2021, M. Ehrhardt and M. Günther (eds.), pp. 373-380, Mathematics in Industry 39, Springer, Berlin, Heidelberg, 2022. (arXiv:2107.09094)
- B. Düring, N. Georgiou, S. Merino-Aceituno and E. Scalas. Continuum and thermodynamic limits for a simple random-exchange model. Stochastic Process. Appl. 149 (2022), 248-277. (arXiv:2003.00930)
- B. Düring, M. Fischer and M.-T. Wolfram. An Elo-type rating model for players and teams of variable strength. Phil. Trans. R. Soc. A 380 (2022), 20210155. (arXiv:2109.15046)
- B. Düring and O. Wright. On a kinetic opinion formation model for pre-election polling. Phil. Trans. R. Soc. A 380 (2022), 20210154. (arXiv:2107.05964)
- J.A. Carrillo, B. Düring, L.M. Kreusser and C.-B. Schönlieb. Equilibria of an anisotropic nonlocal interaction equation: analysis and numerics. Discrete Contin. Dyn. Syst. Ser. A 41(8) (2021), 3985-4012. (arXiv:1912.093376)
- B. Düring, N. Georgiou, S. Merino-Aceituno and E. Scalas. Continuum and thermodynamic limits for a wealth-distribution model. In: Complexity, Heterogeneity, and the Methods of Statistical Physics in Economics, pp.79-99, H. Aoyama et al. (eds.), Evolutionary Economics and Social Complexity Science 22, Springer, Singapore, 2020.
- J.A. Carrillo, B. Düring, L.M. Kreusser and C.-B. Schönlieb. Stability analysis of line patterns of an anisotropic interaction model. SIAM J. Appl. Dyn. Syst. 18(4) (2019), 1798–1845. (arXiv:1806.04966)
- B. Düring and A. Pitkin. High-order compact finite difference scheme for option pricing in stochastic volatility with contemporaneous jump models. In: Progress in Industrial Mathematics at ECMI 2018, I. Faragó et al. (eds.), pp. 365-371, Mathematics in Industry 30, Springer, Berlin, Heidelberg, 2019. (arXiv:1810.13248)
- B. Düring and A. Pitkin. High-order compact finite difference scheme for option pricing in stochastic volatility jump models. J. Comput. Appl. Math. 355 (2019), 201-217. (arXiv:1704.05308)
- B. Düring, C. Gottschlich, S. Huckemann, L.M. Kreusser and C.-B. Schönlieb. An anisotropic interaction model for simulating fingerprints. J. Math. Biol. 78(7) (2019), 2171-2206. (arXiv:1711.07417)
- B. Düring, M. Torregrossa and M.-T. Wolfram. Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects. J. Nonlinear Sci. 29(3) (2019), 1095-1128. (arXiv:1806.06648)
- B. Düring and A. Pitkin. Efficient hedging in Bates model using high-order compact finite differences. In: Recent Advances in Mathematical and Statistical Methods, D.M. Kilgour et al. (eds.), pp. 489-498, Springer Proceedings in Mathematics & Statistics 259, Springer, Cham, 2018. (arXiv:1710.05542)
- B. Düring, L. Pareschi and G. Toscani. Kinetic models for optimal control of wealth inequalities. Eur. Phys. J. B 91(10) (2018), 265. (arXiv:1803.02171)
- J.A. Carrillo, B. Düring, D. Matthes and D.S. McCormick. A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes. J. Sci. Comput. 75(3) (2018), 1463-1499. (arXiv:1702.01707)
- M. Burger, B. Düring, L.M. Kreusser, P.A. Markowich and C.-B. Schönlieb. Pattern formation of a nonlocal, anisotropic interaction model. Math. Models Methods Appl. Sci. 28(3) (2018), 409-451. (arXiv:1610.08108)
- B. Düring, C. Hendricks and J. Miles. Sparse grid high-order ADI scheme for option pricing in stochastic volatility models. In: Novel Methods in Computational Finance, M. Ehrhardt et al. (eds.), pp. 295-312, Mathematics in Industry 25, Springer, Cham, 2017. (arXiv:1611.01379)
- B. Düring and C. Heuer. Essentially high-order compact schemes with application to stochastic volatility models on non-uniform grids. In: Novel Methods in Computational Finance, M. Ehrhardt et al. (eds.), pp. 313-319, Mathematics in Industry 25, Springer, Cham, 2017. (arXiv:1611.00316)
- B. Düring, N. Georgiou and E. Scalas. A stylised model for wealth distribution. In: Economic Foundations for Social Complexity Science, Y.Aruka, A. Kirman (eds.), pp. 135-157, Evolutionary Economics and Social Complexity Science 9, Springer, Singapore, 2017. (arXiv:1609.08978)
- B. Düring. Partial differential equations model political segregation. SIAM News Blog, 8 June 2017.
- B. Düring and J. Miles. High-order ADI scheme for option pricing in stochastic volatility models. J. Comput. Appl. Math. 316 (2017), 109-121. (arXiv:1512.02529)
- B. Düring, A. Jüngel and L. Trussardi. A kinetic equation for economic value estimation with irrationality and herding. Kinet. Relat. Models 10(1) (2017), 239-261. (arXiv:1601.03244)
- B. Düring, C.-B. Schönlieb and M.-T. Wolfram (eds.). Gradient flows: from theory to application. ESAIM Proc. Surveys No. 54, EDP Sciences, France, 2016.
- B. Düring and C. Heuer. High-order compact schemes for Black-Scholes basket options. In: Progress in Industrial Mathematics at ECMI 2014, G. Russo et al. (eds.), pp. 1095-1102, Mathematics in Industry 22, Springer, Berlin, Heidelberg, 2016. (arXiv:1505.07613)
- B. Düring, P. Fuchs and A. Jüngel. A higher-order gradient flow scheme for a singular one-dimensional diffusion equation. Preprint. (arXiv:1509.00384)
- B. Düring and M.-T. Wolfram. Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation. Proc. R. Soc. Lond. A 471 (2015), 20150345. (arXiv:1505.07433)
- B. Düring and C. Heuer. High-order compact schemes for parabolic problems with mixed derivatives in multiple space dimensions. SIAM J. Numer. Anal. 53(5) (2015), 2113-2134. (arXiv:1506.06711)
- B. Düring, M. Fournié and C. Heuer. High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. J. Comput. Appl. Math. 271 (2014), 247-266. (arXiv:1404.5138)
- L. Calatroni, B. Düring and C.-B. Schönlieb. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. Discrete Contin. Dyn. Syst. Ser. A 34(3) (2014), 931-957. (arXiv:1305.5362)
- B. Düring, M. Fournié and A. Rigal. High-order ADI schemes for convection-diffusion equations with mixed derivative terms. In: Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM'12, Selected papers from the ICOSAHOM 12 conference, June 25-29, 2012, Gammarth, Tunisia, M. Azaïez et al. (eds.), pp. 217-226, Lecture Notes in Computational Science and Engineering 95, Springer, Berlin, Heidelberg, 2013. (arXiv:1505.07621)
- M. Benning, L. Calatroni, B. Düring and C.-B. Schönlieb. A primal-dual approach for a total variation Wasserstein flow. In: Geometric Science of Information, First International Conference, GSI 2013, Paris, France, August 28-30, 2013, F. Nielsen and F. Barbaresco (eds.), pp. 413-421, Lecture Notes in Computer Science 8085, Springer, 2013. (arXiv:1305.5368)
- B. Düring and M. Fournié. High-order compact finite difference scheme for option pricing in stochastic volatility models. J. Comput. Appl. Math. 236(17) (2012), 4462-4473. (arXiv:1404.5140)
- B. Düring and C.-B. Schönlieb. A high-contrast fourth-order PDE from imaging: numerical solution by ADI splitting. In: Multi-scale and High-Contrast Partial Differential Equations, H. Ammari et al. (eds.), pp. 93-103, Contemporary Mathematics 577, American Mathematical Society, Providence, 2012.
- B. Düring and M. Fournié. On the stability of a compact finite difference scheme for option pricing. In: Progress in Industrial Mathematics at ECMI 2010, M. Günther et al. (eds.), pp. 215-221, Mathematics in Industry 17, Springer, Berlin, Heidelberg, 2012.
- B. Düring. Kinetic modelling of opinion leadership. SIAM News 44(10), December 2011, pp. 1, 8.
- B. Düring, D. Matthes and J.-P. Milisic. A gradient flow scheme for nonlinear fourth order equations. Discrete Contin. Dyn. Syst. Ser. B 14(3) (2010), 935-959.
- B. Düring and D. Matthes. A mathematical theory for wealth distribution. In: Mathematical modeling of collective behavior in socio-economic and life-sciences, G. Naldi et al. (eds.), pp. 81-113, Birkhäuser, Boston, 2010.
- B. Düring. Multi-species models in econo- and sociophysics. In: Econophysics & Economics of Games, Social Choices and Quantitative Techniques, B. Basu et al. (eds.), pp. 83-89, Springer, Milan, 2010.
- B. Düring and M. Fournié. Compact finite difference scheme for option pricing in Heston's model. In: AIP Conference Proceedings 1281, Numerical Analysis and Applied Mathematics: International Conference of Numerical Analysis and Applied Mathematics 2010, T.E. Simos et al. (eds.), pp. 219-222, American Institute of Physics (AIP), Melville, NY, 2010.
- B. Düring, P.A. Markowich, J.-F. Pietschmann and M.-T. Wolfram. Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders.
Proc. R. Soc. Lond. A 465(2112) (2009), 3687-3708. - B. Düring, D. Matthes and G. Toscani. A Boltzmann-type approach to the formation of wealth distribution curves. Riv. Mat. Univ. Parma (8) 1 (2009), 199-261.
- B. Düring. Asset pricing under information with stochastic volatility. Rev. Deriv. Res. 12(2) (2009), 141-167.
- B. Düring and G. Toscani. International and domestic trading and wealth distribution. Comm. Math. Sci. 6(4) (2008), 1043-1058.
- B. Düring, A. Jüngel and S. Volkwein. Sequential quadratic programming method for volatility estimation in option pricing. J. Optim. Theory Appl. 139(3) (2008), 515-540.
- B. Düring, D. Matthes and G. Toscani. Kinetic equations modelling wealth redistribution: a comparison of approaches. Phys. Rev. E 78(5) (2008), 056103.
- B. Düring. Calibration problems in option pricing. In: Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing, M. Ehrhardt (ed.), pp. 323-352, Nova Sci. Publ., Inc., Hauppauge, NY, 2008.
- B. Düring, D. Matthes and G. Toscani. Exponential and algebraic relaxation in kinetic models for wealth distribution. In: "WASCOM 2007" - Proceedings of the 14th Conference on Waves and Stability in Continuous Media, N. Manganaro et al. (eds.), pp. 228-238, World Sci. Publ., Hackensack, NJ, 2008.
- B. Düring and G. Toscani. Hydrodynamics from kinetic models of conservative economies. Physica A 384(2) (2007), 493-506.
- B. Düring. A semi-smooth Newton method for an inverse problem in option pricing. Proc. Appl. Math. Mech. 7(1) (2007), Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, 1081105-1081106.
- B. Düring and E. Lüders. Option prices under generalized pricing kernels. Rev. Deriv. Res. 8(2) (2005), 97-123.
- B. Düring and A. Jüngel. Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets. Nonl. Anal. TMA 62(3) (2005), 519-544.
- B. Düring, M. Fournié and A. Jüngel. Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation. Math. Mod. Num. Anal. 38(2) (2004), 359-369.
- B. Düring, M. Fournié and A. Jüngel. High-order compact finite difference schemes for a nonlinear Black-Scholes equation. Intern. J. Theor. Appl. Finance 6(7) (2003), 767-789.
