Probabilistic Representations of Nonlocal Nonlinear PDEs via Branching Diffusions with Jumps
28 Pages Posted: 11 Sep 2019
Date Written: September 10, 2019
We extend the branching diffusion Monte Carlo method of Henry-Labordère et al.  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
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