Computation of the Survival Probability of Brownian Motion with Drift Subject to an Intermittent Step Barrier

Abstract

This article provides an exact formula for the survival probability of Brownian motion with drift when the absorbing boundary is defined as an intermittent step barrier, i.e., an alternate sequence of time intervals when the boundary is piecewise constant, and time intervals without any defined boundary. Numerical implementation is dealt with by a simple and robust Monte Carlo integration algorithm directly derived from the formula, which compares favorably with conditional Monte Carlo simulation. Exact analytical benchmarks are also provided to assess the accuracy of the numerical implementation.

Keywords

• survival probability
• Brownian motion
• boundary crossing
• first-passage time
• intermittent barrier
• step barrier