On the last zero process with an application in corporate bankruptcy

Baurdoux, Erik J. 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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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
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:	20 Sep 2025 02:51
URI:	http://eprintstest.lse.ac.uk/id/eprint/128366

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