First-passage times of regime switching models

The probability of a stochastic process to first breach an upper and/or a lower level is an important quantity for optimal control and risk management. We present those probabilities for regime switching Brownian motion. In the 2and 3-state model, the Laplace transform of the (single and double barrier) first-passage times is – up to the roots of a polynomial of degree 4 (respectively 6) – derived in closed-form by solving the matrix Wiener-Hopf factorization. This extends single barrier results in the 2-state model by Guo [2001b]. If the quotient of drift and variance is constant over all states, we show that the Laplace transform can even be inverted analytically.