# Seminar Event Detail

Financial/Actuarial Mathematics

 Date:  Wednesday, February 07, 2018 Location:  1360 East Hall (4:00 PM to 5:00 PM) Title:  Multilevel Picard approximations for high-dimensional nonlinear parabolic partial differential equations Abstract:   In this talk we present a family of new approximation methods for high-dimensional PDEs and BSDEs. A key idea of our methods is to combine multilevel approximations with Picard fixed-point approximations. Thereby we obtain a class of multilevel Picard approximations. Our error analysis proves that for semi-linear 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 $\eps\in(0,\infty)$ 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 Allen-Cahn equation) and financial engineering (such as derivative pricing incorporating default risks) in the case of $d=100$ space dimensions. Files: Speaker:  Thomas Kruse Institution:  University of Duisburg-Essen Event Organizer: