Unbiased simulation method with the poisson kernel method for stochastic differential equations with reflection

Abstract

We consider unbiased simulation methods for one-dimensional stochastic differential equations with reflection at zero. In particular, we propose improvements of the forward unbiased simulation method provided by Alfonsi et al. (Parametrix methods for one-dimensional reflected SDEs. Modern problems of stochastic analysis and statistics: selected contributions in honor of Valentin Konakov. Springer, pp 43–66, 2017). In this paper, we will apply the Poisson kernel method to improve the negativity and high variance problems of the associated simulation method. We also discuss some choices for the behavior of the approximation process near the boundary. This improvement is demonstrated through some numerical experiments.