Article

During, Bertram, Georgiou, Nicos, Merino-Aceituno, Sara and Scalas, Enrico (2022) Continuum and thermodynamic limits for a simple random-exchange model. Stochastic Processes and their Applications, 149. pp. 248-277. ISSN 0304-4149

Carrilo, José A, Düring, Bertram, Kreusser, Lisa Maria and Schöenlieb, Carola-Bibiane (2019) Stability analysis of line patterns of an anisotropic interaction model. SIAM Journal on Applied Dynamical Systems, 18 (4). pp. 1798-1845. ISSN 1536-0040

Düring, Bertram and Pitkin, Alexander (2019) High-order compact finite difference scheme for option pricing in stochastic volatility jump models. Journal of Computational and Applied Mathematics, 355. pp. 201-217. ISSN 0377‐0427

Düring, Bertram, Torregrossa, Marco and Wolfram, Marie-Therese (2019) Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects. Journal of Nonlinear Science, 29 (3). pp. 1095-1128. ISSN 0938-8974

Düring, Bertram, Gottschlich, Carsten, Huckemann, Stephan, Kreusser, Lisa Maria and Schönlieb, Carola-Bibiane (2019) An anisotropic interaction model for simulating fingerprints. Journal of Mathematical Biology, 78 (7). pp. 2171-2206. ISSN 0303-6812

D¨uring, Bertram, Pareschi, Lorenzo and Toscani, Giuseppe (2018) Kinetic models for optimal control of wealth inequalities. European Physical Journal B: Condensed Matter and Complex Systems, 91 (10). 265 1-12. ISSN 1434-6028

Carrillo, José A, Düring, Bertram, Matthes, Daniel and McCormick, David S (2018) A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes. Journal of Scientific Computing, 75 (3). pp. 1463-1499. ISSN 0885-7474

Burger, Martin, Düring, Bertram, Kreusser, Lisa Maria, Markowich, Peter A and Schönlieb, Carola-Bibiane (2018) Pattern formation of a nonlocal, anisotropic interaction model. Mathematical Models and Methods in Applied Sciences, 28 (3). pp. 409-451. ISSN 0218-2025

Düring, Bertram, Jüngel, Ansgar and Trussardi, Lara (2017) A kinetic equation for economic value estimation with irrationality and herding. Kinetic and Related Models, 10 (1). pp. 239-261. ISSN 1937-5093

Düring, Bertram and Miles, James (2016) High-order ADI scheme for option pricing in stochastic volatility models. Journal of Computational and Applied Mathematics, 316. pp. 109-121. ISSN 0377-0427

Düring, Bertram and Wolfram, Marie-Therese (2015) Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 471 (2182). ISSN 1364-5021

Düring, Bertram and Heuer, Christof (2015) High-order compact schemes for parabolic problems with mixed derivatives in multiple space dimensions. SIAM Journal on Numerical Analysis, 53 (5). pp. 2113-2134. ISSN 0036-1429

Düring, Bertram, Fournié, Michel and Heuer, Christof (2014) High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. Journal of Computational and Applied Mathematics, 271. pp. 247-266. ISSN 0377-0427

Calatroni, Luca, Düring, Bertram and Schönlieb, Carola-Bibiane (2014) ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. Discrete and Continuous Dynamical Systems - Series A, 34 (3). pp. 931-957. ISSN 1078-0947

Düring, Bertram and Fournié, Michel (2012) High-order compact finite difference scheme for option pricing in stochastic volatility models. Journal of Computational and Applied Mathematics, 236 (17). pp. 4462-4473. ISSN 0377-0427

Düring, B (2011) Kinetic modelling of opinion leadership. SIAM News, 44 (10). pp. 1-8. ISSN 0036-1437

Düring, Bertram, Matthes, Daniel and Milišić, Josipa Pina (2010) A gradient flow scheme for nonlinear fourth order equations. Discrete and Continuous Dynamical Systems - Series B, 14 (3). pp. 935-959. ISSN 1531-3492

Düring, Bertram, Markowich, Peter, Pietschmann, Jan-Frederik and Wolfram, Marie-Therese (2009) Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proceedings A: Mathematical, Physical and Engineering Sciences, 465 (211). pp. 3687-3708. ISSN 1364-5021

Düring, Bertram, Matthes, Daniel and Toscani, Giuseppe (2009) A Boltzmann-type approach to the formation of wealth distribution curves. Rivista di Matematica della Università di Parma, 8 (1). pp. 199-261. ISSN 0035-6298

Düring, Bertram (2009) Asset pricing under information with stochastic volatility. Review of Derivatives Research, 12 (2). pp. 141-167. ISSN 1380-6645

Düring, Bertram and Toscani, Giuseppe (2008) International and domestic trading and wealth distribution. Communications in Mathematical Sciences, 6 (4). pp. 1043-1058. ISSN 1539-6746

Düring, B, Jüngel, A and Volkwein, S (2008) Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing. Journal of Optimization Theory and Applications, 139 (3). pp. 515-540. ISSN 0022-3239

Düring, Bertram, Matthes, Daniel and Toscani, Giuseppe (2008) Kinetic equations modelling wealth redistribution: a comparison of approaches. Physical Review E, 78 (5). ISSN 1539-3755

Düring, B and Toscani, G (2007) Hydrodynamics from kinetic models of conservative economies. Physica A: Statistical Mechanics and its Applications, 384 (2). pp. 493-506. ISSN 0378-4371

Düring, Bertram and Jüngel, Ansgar (2005) Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets. Nonlinear Analysis, 62 (3). pp. 519-544.

Düring, Bertram and Lüders, Erik (2005) Option prices under generalized pricing kernels. Review of Derivatives Research, 8 (2). pp. 97-123.

Düring, Bertram, Fournié, Michel and Jüngel, Ansgar (2004) Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation. ESAIM: Mathematical Modelling and Numerical Analysis, 38. pp. 359-369. ISSN 0764-583X

Düring, Bertram, Fournié, Michel and Jüngel, Ansgar (2003) High-order compact finite difference schemes for a nonlinear Black-Scholes equation. International Journal of Theoretical and Applied Finance, 6 (7). pp. 767-789. ISSN 0219-0249

Book Section

Düring, Bertram, Georgiou, Nicos, Merino-Aceituno, Sara and Scalas, Enrico (2020) Continuum and thermodynamic limits for a wealth-distribution model. In: Aoyama, Hideaki, Aruka, Yuji and Yoshikawa, Hiroshi (eds.) Complexity, heterogeneity, and the methods of statistical physics in economics: essays in memory of Masanao Aoki. Evolutionary Economics and Social Complexity Science, 22 . Springer, pp. 79-99. ISBN 9789811548055

Düring, Bertram and Pitkin, Alexander (2019) High-order compact finite difference scheme for option pricing in stochastic volatility with contemporaneous jump models. In: Faragó, István, Izsák, Ferenc and Simon, Péter L (eds.) Progress in Industrial Mathematics at ECMI 2018. The European Consortium for Mathematics in Industry . Springer Verlag. ISBN 9783030275495

During, Bertram, Georgiou, Nicos and Scalas, Enrico (2017) A stylised model for wealth distribution. In: Akura, Yuji and Kirman, Alan (eds.) Economic Foundations of Social Complexity Science. Springer Singapore, Singapore, pp. 95-117. ISBN 9789811057045

Dűring, Bertram and Heuer, Christof (2017) Essentially high-order compact schemes with application to stochastic volatility models on non-uniform grids. In: Erhhardt, Matthias, Gunther, Michael and ter Maten, E. Jan W (eds.) Novel Methods of Computational Finance. The European Consortium of Mathematics in Industry, 25 . Springer International, pp. 313-319. ISBN 9783319612829

Düring, Bertram, Miles, James and Hendricks, Christian (2017) Sparse grid high-order ADI scheme for option pricing in stochastic volatility models. In: Erhhardt, Matthias, Gunther, Michael and ter Maten, E. Jan W. (eds.) Novel Methods of Computational Finance. The European Consortium of Mathematics in Industry, 25 . Springer International, pp. 295-312. ISBN 9783319612829

Düring, Bertram and Heuer, Christof (2015) High-order compact schemes for Black-Scholes basket options. In: Progress in industrial mathematics at ECMI 2014. Mathematics in industry . Springer. ISBN 9783642427596

Düring, Bertram, Fournié, Michel and Rigal, Alain (2013) High-order ADI schemes for convection-diffusion equations with mixed derivative terms. In: Azaïez, Mejdi, Hesthaven, Jan S. and El Fekih, Henda (eds.) Spectral and high order methods for partial differential equations - ICOSAHOM ' 12. Lecture notes in computational science and engineering (95). Springer-Verlag, Berlin, pp. 217-226. ISBN 9783319016009

Benning, Martin, Calatroni, Luca, Düring, Bertram and Schönlieb, Carola-Bibiane (2013) A primal-dual approach for a total variation Wasserstein flow. In: Nielsen, Frank and Barbaresco, Frédéric (eds.) Geometric science of information: first international conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings. Lecture notes in computer science (8085). Springer Berlin Heidelberg, Berlin, pp. 413-421. ISBN 9783642400193

Düring, Bertram and Fournié, Michel (2012) On the stability of a compact finite difference scheme for option pricing. In: Günther, Michael, Bartels, Andreas, Brunk, Markus, Schöps, S and Striebel, M (eds.) Progress in industrial mathematics at ECMI 2010. Mathematics in industry, 17 (3). Springer, Berlin, Heidelberg, pp. 215-221. ISBN 978-3642250996

Düring, Bertram and Schönlieb, Carola-Bibiane (2012) A high-contrast fourth-order PDE from imaging: numerical solution by ADI splitting. In: Ammari, Habib, Capdeboscq, Yves and Kang, Hyeonbae (eds.) Multi-scale and high-contrast partial differential equations: from modelling, to mathematical analysis, to inversion. Contemporary Mathematics, 577 . American Mathematical Society, Providence, pp. 93-104. ISBN 9780821869291

Düring, Bertram (2010) Multi-species models in econo- and sociophysics. In: Basu, B, Chakrabarti, BK, Chakravarty, SR and Gangopadhyay, K (eds.) Econophysics & Economics of Games, Social Choices and Quantitative Techniques. Springer, Dordrecht, pp. 83-89. ISBN 9788847015005

Düring, Bertram and Matthes, Daniel (2010) A mathematical theory for wealth distribution. In: Naldi, G, Pareschi, L and Toscani, G (eds.) Mathematical modeling of collective behavior in socio-economic and life-sciences. Birkhäuser, pp. 81-113. ISBN 978-0-8176-4945-6

Düring, Bertram (2009) Calibration problems in option pricing. In: Ehrhardt, M (ed.) Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing. Nova Science Publishers, pp. 323-352. ISBN 9781604569315

Conference or Workshop Item

Düring, Bertram and Fournié, Michel (2010) Compact finite difference scheme for option pricing in Heston's model. In: 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., Rhodes, Greece.

Düring, B, Matthes, D and Toscani, G (2008) 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., Sicily, Italy.

Düring, Bertram (2007) A semi-smooth Newton method for an inverse problem in option pricing. In: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, 2007, Zürich.

Conference Proceedings

Düring, Bertram and Pitkin, Alexander (2018) Efficient hedging in Bates model using high-order compact finite differences. The 5th AMMCS International Conference, Waterloo, Ontario, Canada, August 18-23, 2019. Published in: Makarov, Roman, (ed.) Recent Advances in Mathematical and Statistical Methods for Scientific and Engineering Applications. 259 489-498. Springer Verlag ISSN 2194-1009

Edited Book

Düring, Bertram, Schönlieb, Carola-Bibiane and Wolfram, Wolfram, eds. (2016) Gradient flows: from theory to application. ESAIM: Proceedings and Surveys, 54 . EDP Sciences, SMAI.

Thesis

Düring, Bertram (2005) Black-Scholes type equations: mathematical analysis, parameter identification & numerical solution. Doctoral thesis (PhD), J. Gutenberg-Universität Mainz, Germany.