Probabilistic Representations of Nonlocal Nonlinear PDEs via Branching Diffusions with Jumps

28 Pages Posted: 11 Sep 2019

See all articles by Christoph Belak

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Daniel Hoffmann

University of Trier

Frank Thomas Seifried

University of Trier

Date Written: September 10, 2019

Abstract

We extend the branching diffusion Monte Carlo method of Henry-Labordère et al. [2019] to the case of parabolic PDEs with non-local polynomial non-linearities. We investigate branching diffusion representations of classical solutions, and we provide sufficient conditions under which the branching diffusion representation solves the PDE in the viscosity sense. Our theoretical setup directly leads to a Monte Carlo algorithm, whose applicability is showcased in a high-dimensional example. As a second application, we compute credit valuation adjustments for systemic counterparties in a jump-diffusion model.

Keywords: Branching Diffusion, Nonlocal PDE, Nonlinear Jumps, Monte Carlo Simulation, Credit Valuation Adjustment

Suggested Citation

Belak, Christoph and Hoffmann, Daniel and Seifried, Frank Thomas, Probabilistic Representations of Nonlocal Nonlinear PDEs via Branching Diffusions with Jumps (September 10, 2019). Available at SSRN: https://ssrn.com/abstract=3451280 or http://dx.doi.org/10.2139/ssrn.3451280

Christoph Belak (Contact Author)

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Daniel Hoffmann

University of Trier ( email )

15, Universitaetsring
Trier, 54286
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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