Date: Wednesday, February 07, 2018
Location: 1360 East Hall (4:00 PM to 5:00 PM)
Title: Multilevel Picard approximations for highdimensional nonlinear parabolic partial differential equations
Abstract: In this talk we present a family of new approximation methods for highdimensional PDEs and BSDEs. A key idea of our methods is to combine multilevel approximations with Picard fixedpoint approximations. Thereby we obtain a class of multilevel Picard approximations. Our error analysis proves that for semilinear heat equations, the computational complexity of one of the proposed methods is bounded by $O(d,eps^{(4+delta)})$ for any $delta > 0$, where $d$ is the dimensionality of the problem and
$epsin(0,infty)$ is the prescribed accuracy. We illustrate the efficiency of one of the proposed approximation methods by means of numerical simulations presenting approximation accuracy against runtime for several nonlinear PDEs from physics (such as the AllenCahn equation) and financial engineering (such as derivative pricing incorporating default risks) in the case of $d=100$ space dimensions.
Files: 4736_kruse.pdf
Speaker: Thomas Kruse
Institution: University of DuisburgEssen
Event Organizer:
