Andreas Neuenkirch

Raum B 107, Gebäude A5, 6

Tel.: +49  621 181-2454

E-mail: neuenkirch(at)math.uni-mannheim.de

Sprechstunde:  n.V. (via E-mail)

Forschungsinteressen

Numerische Methoden für Stochastische Prozesse, Monte Carlo Methoden, Information Based Complexity, Stochastische Analysis

Meine aktuelle Forschung konzentriert sich auf Numerische Verfahren für stochastische Differentialgleichungen bzgl. der Brownschen oder der fraktionalen Brownschen Bewegung.  Bei letzteren Gleichungen bin ich auch an ihrem Langzeitverhalten,  statistischen oder anderen Eigenschaften interessiert.

Viele der betrachteten Gleichungen haben Anwendungen in der Finanzmathematik, Biologie oder anderen Gebieten.

Ich bin Associate Editor des Journal of Complexity und Mitglied des DFG-Graduiertenkolleg 1953 "Statistical Modeling of Complex Systems and Processes". Weiterhin war ich Mitglied des DFG-Schwerpunktprogramms 1324.

Working Papers

  • Simone Göttlich, Kerstin Lux and Andreas Neuenkirch. The Euler scheme for stochastic differential equations with discontinuous drift coefficient: A numerical study of the convergence rate, 2017. arxiv preprint.
  • Andreas Neuenkirch and Taras Shalaiko. The order barrier for strong approximation of rough volatility models, 2016. arxiv preprint.

Publikationen (2012 - heute)

  1. L.H. Duc, M.J. Garrido-Atienza, A. Neuenkirch, B. Schmalfuß. Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2,1), Journal of Differential Equations, to appear
  2. Andreas Neuenkirch, Maria Jose Garrido-Atienza and Björn Schmalfuß. Asymptotic stability of differential equations driven by Hölder-continuous paths,  Journal of Dynamics and Differential Equations, to appear
  3. Martin Altmayer and Andreas Neuenkirch. Discretizing the Heston Model: An Analysis of the Weak Convergence Rate. IMA Journal of Numerical Analysis, 2017, 37(4), 1930-1960
  4. Andreas Neuenkirch and Peter Parczewski. Optimal Approximation of Skorohod integrals, Journal of Theoretical Probability, to appear
  5. Taras Shalaiko and Andreas Neuenkirch. The maximum rate of convergence for the approximation of the fractional Lévy area at a single point. Journal of Complexity, 2016, 33, 107-117
  6. Taras Shalaiko and Andreas Neuenkirch.  The Relation Between Mixed and Rough SDEs and Its Application to Numerical Methods. Stochastic Analysis and Applications, 2015, 33(3),  927-942
  7. Martin Altmayer and Andreas Neuenkirch. Multilevel Monte Carlo Quadrature of Discontinuous Payoffs in the Generalized Heston Model Using Malliavin Integration by Parts. Siam Journal of Financial Mathematics, 2015, 6(1), 22–52
  8. Bahareh Akhtari, Esmail Babolian and Andreas Neuenkirch. An Euler Scheme for Stochastic Delay Differential Equations on Unbounded Domains: Pathwise Convergence.  Discrete and Continuous Dynamical Systems - Series B, 2015, 20(1), 23 - 38
  9. Andreas Neuenkirch and Lukasz Szpruch. First Order Strong Approximations of Scalar SDEs Defined in a Domain. Numerische Mathematik, 2014, 128(1), 103-136
  10. Andreas Neuenkirch and Samy Tindel. A Least Square-Type Procedure for Parameter Estimation in SDEs with Additive Fractional Noise. Statistical Inference for Stochastic Processes, 2014, 17(1),  99-120
  11. Peter Kloeden and Andreas Neuenkirch. Convergence of Numerical Methods for Stochastic Differential Equations in Mathematical Finance. In: Recent Developments in Computational Finance: Foundations, Algorithms and Applications, T. Gerstner and P.E. Kloeden (eds), Interdisciplinary Mathematical Sciences Series, Vol. 14, World Scientific Publishing, Singapur, 2013; pp. 49-80
  12. Steffen Dereich, Andreas Neuenkirch and Lukas Szpruch. An Euler-Type Method for the Strong Approximation of the Cox-Ingersoll-Ross Process. Proceedings of the Royal Society, 2012, 468, 1105-1115
  13. Aurélien Deya, Andreas Neuenkirch and Samy Tindel. A Milstein-Type Scheme without Lévy Area Terms for SDEs Driven by Fractional Brownian Motion. Annales de l’Institut Henri Poincaré, 2012, 48(2), 518–550

 

 

Für eine vollständige Liste, siehe z.B. Google Scholar oder das Zentralblatt.