On the first passage time under regime-switching with jumps. (English) Zbl 1402.60106
Kabanov, Yuri (ed.) et al., Inspired by finance. The Musiela Festschrift. Cham: Springer (ISBN 978-3-319-02068-6/hbk; 978-3-319-02069-3/ebook). 387-410 (2014).
Summary: 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.
For the entire collection see [Zbl 1278.91008].
For the entire collection see [Zbl 1278.91008].
MSC:
| 60J75 | Jump processes (MSC2010) |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
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