On the first passage time under regime-switching with jumps

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Inspired by Finance: The Musiela Festschrift, 2014, pp. 387 - 410
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© Springer International Publishing Switzerland 2014. All rights are reserved. In this paper, we present the analytical solution for the Laplace transform of the joint distribution of the first passage time and undershoot/overshoot value under a regime-switching jump-diffusion model. With the help of some martingale technique, the Laplace transform of the first passage time becomes the solution of a system of linear equations. The methodology discussed here is fairly elementary and can be applied to many stopping-time problems under a regime-switching model with jump risks. Some numerical examples are given to demonstrate the usefulness of our method.
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