Baurdoux, Erik J. ORCID: 0000-0002-5407-0683 and Pedraza, José M.
(2025)
On the last zero process with an application in corporate bankruptcy.
Advances in Applied Probability.
ISSN 0001-8678
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Text (On_the_last_zero_process_with_an_application_in_corporate_bankruptcy)
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Abstract
For a spectrally negative L´evy process X, consider gt, the last time X is below the level zero before time t ≥ 0. We use a perturbation method for L´evy processes to derive an Itˆo formula for the threedimensional process {(gt, t,Xt), t ≥ 0} and its infinitesimal generator. Moreover, with Ut := t − gt, the length of a current positive excursion, we derive a general formula that allows us to calculate a functional of the whole path of (U,X) = {(Ut,Xt), t ≥ 0} in terms of the positive and negative excursions of the process X. As a corollary, we find the joint Laplace transform of (Ueq ,Xeq ), where eq is an independent exponential time, and the q-potential measure of the process (U,X). Furthermore, using the results mentioned above, we find a solution to a general optimal stopping problem depending on (U,X) with an application in corporate bankruptcy. Lastly, we establish a link between the optimal prediction of g∞ and optimal stopping problems in terms of (U,X) as per Baurdoux and Pedraza (2024).
Item Type: | Article |
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Additional Information: | © 2025 The Author(s) |
Divisions: | Statistics |
Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
Date Deposited: | 12 Jun 2025 09:48 |
Last Modified: | 01 Jul 2025 03:09 |
URI: | http://eprints.lse.ac.uk/id/eprint/128366 |
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