Abstracts

This talk studies the first-passage times of regime switching Brownian motion on an upper and/or a lower level. In the 2- and 3-state model, the Laplace transform of the 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 the one-sided results in the 2-state model by Guo (Methodol Comput Appl Probab 3(2):135–143, 2001a). If the quotient of drift and variance is constant over all states, we show that the Laplace transform can even be inverted analytically.
Due to their analytical tractability and their ability to well explain many empirical phenomena, regime switching models have recently gained remarkable attention. In contrast to Lévy models, they can capture effects like persistently changing long-term trends – a desirable feature especially for long dated contracts in Finance and Insurance. In Finance, the presented results can be used for the pricing and risk management of, for example, barrier or lookback options.