Probability Seminar Bálint Négyesi (TUD, DIAM)

A Novel Method for Solving High-Dimensional Backward Stochastic Differential Equations Using Malliavin Calculus and Deep Learning
  • What Scientific Computing English Not a Seminar
  • When 28-10-2020 from 16:00 to 17:00 (Europe/Amsterdam / UTC100)
  • Where online https://uva-live.zoom.us/j/82915951912
  • Contact Name
  • Add event to calendar iCal

Dear All,

 The next SPIP talk is just around the corner, this time on a Wednesday, 28th October from 16:00-17:00. Our speaker is Bálint Négyesi PhD student from the TU Delft (DIAM) and he will talk about 'A Novel Method for Solving High-Dimensional Backward Stochastic Differential Equations Using Malliavin Calculus and Deep Learning'.
 
Zoom Details:
Topic: SPIP - Bálint Négyesi
Time: Oct 28, 2020 04:00 PM Amsterdam, Berlin, Rome, Stockholm, Vienna

Join Zoom Meeting
https://uva-live.zoom.us/j/82915951912

Meeting ID: 829 1595 1912

Abstract:
Backward Stochastic Differential Equations (BSDEs) are known to be a powerful tool in mathematical modeling due to their inherent connection with second-order parabolic PDEs. The solution to a BSDE is a pair, (Y,Z), of adapted processes, which under some conditions can be viewed as a probabilistic representation of the solution (Y), and the gradient of the solution (Z) of an associate PDE. 
Classical numerical methods face the so-called curse of dimensionality and cannot be used to solve high-dimensional problems. In recent years, multiple approaches have been developed to overcome this computational burden, building on deep learning and showing remarkable empirical success well beyond 10 dimensions. However, such Deep BSDE methods struggle with giving accurate approximations for the Z-process throughout the whole time horizon. In the proposed method, we express the Z-process as the Malliavin derivative of the Y-process, using the Malliavin chain rule. An error analysis is carried out proving the consistency of the algorithms and showing first-order convergence under certain assumptions. Numerical experiments are presented to demonstrate the efficiency of the Malliavin formulation compared to other Deep BSDE solvers.
Feel free to distribute the Zoom link and invite your colleagues or people that might be interested.
 
Looking forward to see you all on Wednesday,
 
The Organizers