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


Speaker:  Thomas Kruse
Institution:  University of Duisburg-Essen

Event Organizer:     


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