An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers

TL;DR

This paper derives an explicit formula for the transition density of skew Brownian motion with drift and barriers, and introduces an exact simulation method for this process.

Contribution

It provides the first explicit representation of the transition density and a rejection sampling method for exact simulation of this stochastic process.

Findings

Explicit transition density formula derived

Rejection sampling method for exact simulation proposed

Facilitates analysis and simulation of skew Brownian motion with barriers

Abstract

In this paper, we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover we propose a rejection method to simulate this density in an exact way.