We extend the branching diffusion Monte Carlo method of Henry-Labordère e.a. [2019] to the case of parabolic PDEs with mixed local-nonlocal analytic nonlinearities. We investigate branching diffusion representations of classical solutions, and we provide sufficient conditions under which the...

Summary We introduce a class of optimal stopping problems in which the gain is at least a fraction of the initial value. From a financial point of view this structure can be seen as a guarantee for the holder of an American option. It turns out that the optimal strategies are of two-sided type...