Photo credit: Anna Logue
Research
Currently, we focus on questions arising in
- stochastic numerics,
- information based complexity,
- stochastic analysis,
in particular, on numerical methods for stochastic differential equations (non-standard assumptions, quadrature problems and lower error bounds).
See also the individual profil pages of each researcher.
Publications of the Chair
- Mickel, A. and Neuenkirch, A. (2023). Sharp L1-approximation of the log-Heston stochastic differential equation by Euler-type methods. The Journal of Computational Finance, 26, 67–100 (forthcoming).
- Mickel, A. and Neuenkirch, A. (2023). The weak convergence order of two Euler-type discretization schemes for the log-Heston model. IMA Journal of Numerical Analysis : IMAJNA (forthcoming).
- Mickel, A. and Neuenkirch, A. (2021). The weak convergence rate of two semi-exact discretization schemes for the Heston model. Risks : Open Access Journal, 9, Article 23.
- Neuenkirch, A. and Szölgyenyi, M. (2021). The Euler-Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem. IMA Journal of Numerical Analysis : IMAJNA, 41, 1164-1196.
- Göttlich, S., Lux, K. and Neuenkirch, A. (2019). The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate. Advances in Difference Equations : ADE, 2019, 1–21.
- Koch, S. and Neuenkirch, A. (2019). The Mandelbrot-van Ness fractional Brownian motion is infinitely differentiable with respect to its Hurst parameter. Discrete and Continuous Dynamical Systems : DCDS. Series B, 24, 3865-3880.
- Neuenkirch, A., Szölgyenyi, M. and Szpruch, L. (2019). An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis. SIAM Journal on Numerical Analysis, 57, 378–403.
- Bender, C. and Parczewski, P. (2018). Discretizing Malliavin calculus. Stochastic Processes and Their Applications, 128, 2489 – 2537.
- Duc, L. H., Garrido-Atienza, M. J., Neuenkirch, A. and Schmalfuß, B. (2018). Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2,1). Journal of Differential Equations, 264, 1119-1145.
- Garrido-Atienza, M. J., Neuenkirch, A. and Schmalfuß, B. (2018). Asymptotical stability of differential equations driven by Hölder continuous paths. Journal of Dynamics and Differential Equations, 30, 359–377.
- Koch, S. (2018). Directional Malliavin derivatives: A characterisation of independence and a generalised chain rule. Communications on Stochastic Analysis, 12, 137–156.
- Neuenkirch, A. and Parczewski, P. (2018). Optimal approximation of skorohod integrals. Journal of Theoretical Probability, 31, 206–231.
- Altmayer, M. and Neuenkirch, A. (2017). Discretising the Heston model: an analysis of the weak convergence rate. IMA Journal of Numerical Analysis : IMAJNA, 37, 1930-1960.
- Parczewski, P. (2017). Donsker-type theorems for correlated geometric fractional Brownian motions and related processes. Electronic Communications in Probability : ECP, 22, 1–13.
- Parczewski, P. (2017). Extensions of the Hitsuda–Skorokhod integral. Communications on Stochastic Analysis, 11, 479–490.
- Parczewski, P. (2017). Optimal approximation of Skorohod integrals – examples with substandard rates. Communications on Stochastic Analysis, 11, 43–61.
- Parczewski, P. (2017). The self-normalized Donsker theorem revisited. Modern Stochastics: Theory and Applications, 4, 189–198.
- Neuenkirch, A. and Shalaiko, T. (2016). The maximum rate of convergence for the approximation of the fractional Lévy area at a single point. Journal of Complexity, 33, 107–117.
- Akhtari, B., Babolian, E. and Neuenkirch, A. (2015). An Euler scheme for stochastic delay differential equations on unbounded domains: pathwise convergence. Discrete and Continuous Dynamical Systems : DCDS. Series B, 20, 23–38.
- Altmayer, M. and Neuenkirch, A. (2015). Multilevel Monte Carlo quadrature of discontinuous payoffs in the generalized Heston model using Malliavin integration by parts. SIAM Journal on Financial Mathematics : SIFIN, 6, 22–52.
- Neuenkirch, A. and Shalaiko, T. (2015). The relation between mixed and rough SDEs and its application to numerical methods. Stochastic Analysis and Applications, 33, 927–942.
- Hinrichs, A., Neuenkirch, A. and Novak, E. (2014). Guest editors' preface. Journal of Complexity, 30, 1.
- Neuenkirch, A. and Szpruch, L. (2014). First order strong approximations of scalar SDEs defined in a domain. Numerische Mathematik, 128, 103–136.
- Parczewski, P. (2014). A Wick functional limit theorem. Probability and Mathematical Statistics, 34, 127–145.
- Parczewski, P. (2014). A fractional Donsker theorem. Stochastic Analysis and Applications, 32, 328–347.
- Dereich, S., Neuenkirch, A. and Szpruch, L. (2012). An Euler-type method for the strong approximation of the Cox-Ingersoll-Ross process. Proceedings / Section A, Mathematics, 468, 1105-1115.
- Deya, A., Neuenkirch, A. and Tindel, S. (2012). A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion. Annales de l'Institut Henri Poincaré. B, Probabilité et statistiques, 48, 518–550.
- Altmayer, M. (2015). Quadrature of discontinuous SDE functionals using Malliavin integration by parts. München: Verlag Dr. Hut.
- Altmayer, M., Dereich, S., Li, S., Müller-Gronbach, T., Neuenkirch, A., Ritter, K. and Yaroslavtseva, L. (2014). Constructive quantization and multilevel algorithms for quadrature of stochastic differential equations. In Extraction of Quantifiable Information from Complex Systems (S. 109–132). Cham: Springer International Publishing.
- Kloeden, P. E. and Neuenkirch, A. (2013). Convergence of numerical methods for stochastic differential equations in mathematical finance. In Recent Developments in Computational Finance (S. 49–80). New Jersey, NJ [u.a.]: World Scientific.
- Bender, C. and Parczewski, P. (2012). On the connection between discrete and continuous Wick calculus with an application to the fractional Black-Scholes model. In Stochastic processes, finance and control : a Festschrift in honor of Robert J. Elliott (S. 3–40). Hackensack, NJ [u.a.]: World Scientific.
- Mickel, A. (2023). Weak and strong approximation of the Log-Heston model by Euler-Type methods and related topics. Dissertation. Mannheim.
- Koch, S. (2019). Sensitivity results in stochastic analysis. Dissertation. Mannheim.
- Altmayer, M. (2015). Quadrature of discontinuous SDE functionals using Malliavin integration by parts. Dissertation. Mannheim.
- Parczewski, P. (2013). A Wick functional limit theorem and applications to fractional Brownian motion. Dissertation. Saarbrücken.
- Neuenkirch, A. (2021). D. Higham, P. Kloeden: “An introduction to the numerical simulation of stochastic differential equations”. Review, Jahresbericht der Deutschen Mathematiker-Vereinigung