Exact Sampling of the Infinite Horizon Maximum of a Random Walk Over a Non-linear Boundary

Jose Blanchet, Jing Dong, Zhipeng Liu

We present the first algorithm that samples ${\max }_{n\ge 0}\{S_n-n^{\alpha }\},$ where $S_n$ is a mean zero random walk, and $n^{\alpha }$ with $\alpha \in (1/2,1)$ defines a nonliner boundary. We show…