Homepage of Bertram Düring

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Publications

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    Books and Book Chapters

  1. 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) (SSRN:2864420)
  2. 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) (SSRN:2862607)
  3. 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.), Evolutionary Economics and Social Complexity Science 9, Springer, Singapore, 2017. (arXiv:1609.08978)
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Preprints

  9. B. Düring, M. Torregrossa and M.-T. Wolfram.
    On a kinetic Elo rating model for players with dynamical strength.
    Submitted for publication. (arXiv:1806.06648)
  10. J.A. Carrillo, B. Düring, L.M. Kreusser and C.-B. Schönlieb.
    Stability analysis of line patterns of an anisotropic interaction model.
    Submitted for publication. (arXiv:1806.04966)
  11. B. Düring, L. Pareschi and G. Toscani.
    Kinetic models for optimal control of wealth inequalities.
    To appear in Eur. Phys. J. B, 2018. (arXiv:1803.02171)
  12. B. Düring, C. Gottschlich, S. Huckemann, L.M. Kreusser and C.-B. Schönlieb.
    An anisotropic interaction model for simulating fingerprints.
    Submitted for publication. (arXiv:1711.07417)
  13. 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.), Springer, 2018. (arXiv:1710.05542) (SSRN:3053759)
  14. B. Düring and A. Pitkin.
    High-order compact finite difference scheme for option pricing in stochastic volatility jump models.
    Submitted for publication. (arXiv:1704.05308) (SSRN:2954523)
  15. Peer-Reviewed Journal Articles

  16. 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)
  17. 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)
  18. 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) (SSRN:2700756)
  19. 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)
  20. 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)
  21. 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) (SSRN:2459861)
  22. 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) (SSRN:2295581)
  23. 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)
  24. 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) (SSRN:1646885)
  25. 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. (preprint)
  26. 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. (SSRN:1399345)
  27. 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. (SSRN:1281404)
  28. B. Düring.
    Asset pricing under information with stochastic volatility.
    Rev. Deriv. Res. 12(2) (2009), 141-167. (SSRN:1212323)
  29. B. Düring and G. Toscani.
    International and domestic trading and wealth distribution.
    Comm. Math. Sci. 6(4) (2008), 1043-1058. (SSRN:1165174)
  30. 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. (SSRN:928219)
  31. B. Düring, D. Matthes and G. Toscani.
    Kinetic equations modelling wealth redistribution: a comparison of approaches.
    Phys. Rev. E 78(5) (2008), 056103. (SSRN:1161019)
  32. B. Düring and G. Toscani.
    Hydrodynamics from kinetic models of conservative economies.
    Physica A 384(2) (2007), 493-506. (preprint)
  33. B. Düring and E. Lüders.
    Option prices under generalized pricing kernels.
    Rev. Deriv. Res. 8(2) (2005), 97-123. (preprint)
  34. 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. (SSRN:520462)
  35. 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. (SSRN:520443)
  36. 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. (SSRN:520162)
  37. Peer-Reviewed Proceedings Papers

  38. 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)
  39. 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)
  40. 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)
  41. 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. (preprint)
  42. 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. (preprint)
  43. 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. (preprint)
  44. 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. (preprint)
  45. 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. (preprint)
  46. Miscellaneous

  47. B. Düring.
    Partial differential equations model political segregation.
    SIAM News Blog, 8 June 2017.
  48. B. Düring, P. Fuchs and A. Jüngel.
    A higher-order gradient flow scheme for a singular one-dimensional diffusion equation.
    Preprint. (arXiv:1509.00384)
  49. B. Düring.
    Kinetic modelling of opinion leadership.
    SIAM News 44(10), December 2011, pp. 1, 8.
  50. B. Düring.
    Agent-based models and diffusive limit equations for socio-economic problems.
    Habilitation thesis, Technische Universität Wien, Austria, 2009.
  51. B. Düring.
    Black-Scholes Type Equations: Mathematical Analysis, Parameter Identification & Numerical Solution.
    Ph.D. thesis, J. Gutenberg-Universität Mainz, Germany, 2005.

    2018

  1. B. Düring, M. Torregrossa and M.-T. Wolfram.
    On a kinetic Elo rating model for players with dynamical strength.
    Submitted for publication. (arXiv:1806.06648)
  2. J.A. Carrillo, B. Düring, L.M. Kreusser and C.-B. Schönlieb.
    Stability analysis of line patterns of an anisotropic interaction model.
    Submitted for publication. (arXiv:1806.04966)
  3. B. Düring, L. Pareschi and G. Toscani.
    Kinetic models for optimal control of wealth inequalities.
    To appear in Eur. Phys. J. B, 2018. (arXiv:1803.02171)
  4. B. Düring, C. Gottschlich, S. Huckemann, L.M. Kreusser and C.-B. Schönlieb.
    An anisotropic interaction model for simulating fingerprints.
    Submitted for publication. (arXiv:1711.07417)
  5. 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.), Springer, 2018. (arXiv:1710.05542) (SSRN:3053759)
  6. B. Düring and A. Pitkin.
    High-order compact finite difference scheme for option pricing in stochastic volatility jump models.
    Submitted for publication. (arXiv:1704.05308) (SSRN:2954523)
  7. 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)
  8. 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)
  9. 2017

  10. 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) (SSRN:2864420)
  11. 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) (SSRN:2862607)
  12. 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.), Evolutionary Economics and Social Complexity Science 9, Springer, Singapore, 2017. (arXiv:1609.08978)
  13. B. Düring.
    Partial differential equations model political segregation.
    SIAM News Blog, 8 June 2017.
  14. 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) (SSRN:2700756)
  15. 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)
  16. 2016

  17. 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.
  18. 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)
  19. 2015

  20. B. Düring, P. Fuchs and A. Jüngel.
    A higher-order gradient flow scheme for a singular one-dimensional diffusion equation.
    Preprint. (arXiv:1509.00384)
  21. 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)
  22. 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) (SSRN:2459861)
  23. 2014

  24. 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) (SSRN:2295581)
  25. 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)
  26. 2013

  27. 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)
  28. 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)
  29. 2012

  30. 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) (SSRN:1646885)
  31. 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. (preprint)
  32. 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. (preprint)
  33. 2011

  34. B. Düring.
    Kinetic modelling of opinion leadership.
    SIAM News 44(10), December 2011, pp. 1, 8.
  35. 2010

  36. 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. (preprint)
  37. 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.
  38. 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.
  39. 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. (preprint)
  40. 2009

  41. 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. (SSRN:1399345)
  42. 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. (SSRN:1281404)
  43. B. Düring.
    Asset pricing under information with stochastic volatility.
    Rev. Deriv. Res. 12(2) (2009), 141-167. (SSRN:1212323)
  44. B. Düring.
    Agent-based models and diffusive limit equations for socio-economic problems.
    Habilitation thesis, Technische Universität Wien, Austria, 2009.
  45. 2008

  46. B. Düring and G. Toscani.
    International and domestic trading and wealth distribution.
    Comm. Math. Sci. 6(4) (2008), 1043-1058. (SSRN:1165174)
  47. 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. (SSRN:928219)
  48. B. Düring, D. Matthes and G. Toscani.
    Kinetic equations modelling wealth redistribution: a comparison of approaches.
    Phys. Rev. E 78(5) (2008), 056103. (SSRN:1161019)
  49. 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.
  50. 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. (preprint)
  51. 2007

  52. B. Düring and G. Toscani.
    Hydrodynamics from kinetic models of conservative economies.
    Physica A 384(2) (2007), 493-506. (preprint)
  53. 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. (preprint)
  54. 2005

  55. B. Düring and E. Lüders.
    Option prices under generalized pricing kernels.
    Rev. Deriv. Res. 8(2) (2005), 97-123. (preprint)
  56. 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. (SSRN:520462)
  57. B. Düring.
    Black-Scholes Type Equations: Mathematical Analysis, Parameter Identification & Numerical Solution.
    Ph.D. thesis, J. Gutenberg-Universität Mainz, Germany, 2005.
  58. 2004

  59. 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. (SSRN:520443)
  60. 2003

  61. 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. (SSRN:520162)