Fast exact simulation of the first-passage event of a subordinator

Abstract: This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-increasing boundary. We prove that the running time of this algorithm has finite moments of all positive orders and give an explicit bound on the expected running time in terms of the L\'evy measure of the subordinator. This bound provides performance guarantees that make our algorithm suitable for Monte Carlo estimation. We provide a GitHub repository with an implementation of the algorithm in Python and Julia.