Numerik und Modellierung nichtlinearer partieller Differentialgleichungen zur Beschreibung von Kredit- und Preisrisiken

• Applicant: Professor Dr. Ansgar Jüngel
• Subject Area: Accounting and Finance
• Term: from 2003 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5470460

• Final Report Year: 2010

Final Report Abstract

No abstract available

Publications

• „Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation"; Mathematical Modelling & Numerical Analysis, 38 (2004), 2; S. 359-369
  B. Düring, M. Fournié, A. Jüngel
  (See online at https://doi.org/10.1051/m2an:2004018)
• „Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets"; Nonlinear Analysis TMA, 62 (2005); S. 519-544
  B. Düring, A. Jüngel
  (See online at https://doi.org/10.1016/j.na.2005.03.068)
• „Option prices under generalized pricing kernels"; Review of Derivatives Research, 8 (2005), 2; S. 97-123
  B. Düring, E. Lüders
  (See online at https://doi.org/10.1007/s11147-005-3852-x)
• „A nonlinear fourth-order parabolic equation a.nd related logarithmic Sobolev inequalities"; Communications in Mathematical Sciences, 4 (2006), S. 275-290
  J. Dolbeault, I. Gentil, A. Jüngel
  (See online at https://doi.org/10.4310/cms.2006.v4.n2.a1)
• „A nonlinear fourth-order parabolic equation with non-homogeneous boundary conditions"; SIAM Journal of Mathematical Analysis, 37 (2006), S. 1761-1779
  M. P. Gualdani, A. Jüngel, G. Toscani
  (See online at https://doi.org/10.1137/S0036141004444615)
• „An algorithmic construction of entropies in higher-order nonlinear PDEs"; Nonlinearity, 19 (2006), S. 633-659
  A. Jüngel, D. Matthes
  (See online at https://doi.org/10.1088/0951-7715/19/3/006)
• „Entropy-energy inequalities and improved convergence rates for nonlinear parabolic equations"; Discrete and Contineous Dynamical Systems B; 6 (2006), S. 1027-1050
  J. A. Carrillo, J. Dolbeault, L Gentil, A. Jüngel
  
• „Hydrodynamics from kinetic models of conservative economies"; Physica A: Statistical Mechanics and its Applications, 384 (2007), 2; S. 493 - 506
  B. Düring, G. Toscani
  (See online at https://doi.org/10.1016/j.physa.2007.05.062)
• „Convergence of an entropic semidiscretization for nonlinear Fokker-Planck equations in Rda; Publicacions Matematiques, 52 (2008), S. 413-433
  J. A. Carrillo, M. P. Gualdani, and A. Jüngel
  
• „International and domestic trading and wealth distribution"; Communications in Mathematical Sciences, 6 (2008), 4; S. 1043 - 1058
  B. Düring, G. Toscani
  (See online at https://dx.doi.org/10.4310/CMS.2008.v6.n4.a12)
• „Kinetic equations modelling wealth redistribution: a comparison of approaches"; Physical Review E, 78 (2008), 5; S. 056103-1 - 056103-12
  B. Düring, D. Matthes, G. Toscani
  (See online at https://doi.org/10.1103/PhysRevE.78.056103)
• „Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing"; Journal of Optimization Theory and Applications, 139 (2008), 3; S. 515-540
  B. Düring, A. Jüngel, S. Volkwein
  (See online at https://doi.org/10.1007/s10957-008-9404-4)
• „A Boltzmann-type approach to the formation of wealth distribution curves"; Rivista di Matematica Università di Parma (Ser. 8), 1 (2009), S. 199-261
  B. Düring, D. Matthes, G. Toscani
  (See online at https://dx.doi.org/10.2139/ssrn.1281404)
• „Asset pricing under information with stochastic volatility"; Review of Derivatives Research, 12 (2009), 2; S. 141 - 107
  B. Düring
  (See online at https://doi.org/10.1007/s11147-009-9031-8)
• „Boltzmann and Fokker- Planck equations triodelling opinion formation in the presence of strong leaders"; Proceedings of the Royal Soci(?ty London A - Mathematical, Physical and Engineering Sciences. 465 (2009), 2112; S. 3687-3708
  B. Düring, P, Markowicli, J. Pietschmann, M. Wolfram
  (See online at https://doi.org/10.1098/rspa.2009.0239)