Branching diffusions with jumps, and valuation with systemic counterparties

We extend the branching diffusion Monte Carlo method of Henry-Labordere e.a. [2019] to case parabolic PDEs with mixed local-nonlocal analytic nonlinearities. investigate representations classical solutions, and we provide sufficient conditions under which representation solves PDE in viscosity sense. Our theoretical setup directly leads a algorithm, whose applicability is showcased stylized high-dimensional example. As our main application, demonstrate how methodology can be used value financial positions defaultable, systemically important counterparties.