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On the last zero process with an application in corporate bankruptcy

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  • Baurdoux, Erik J.
  • Pedraza, José M.

Abstract

For a spectrally negative Lévy process X, consider and its infinitesimal generator. Moreover, with , the last time X is below the level zero before time the length of a current positive excursion, we derive a general formula that allows us to calculate a functional of the whole path of . We use a perturbation method for Lévy processes to derive an Itô formula for the three-dimensional process in terms of the positive and negative excursions of the process X. As a corollary, we find the joint Laplace transform of , where 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 and optimal stopping problems in terms of (U, X) as per Baurdoux, E. J. and Pedraza, J. M., optimal prediction of the last zero of a spectrally negative Lévy process, Annals of Applied Probability, 34 (2024), 1350–1402.

Suggested Citation

  • Baurdoux, Erik J. & Pedraza, José M., 2025. "On the last zero process with an application in corporate bankruptcy," LSE Research Online Documents on Economics 128366, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:128366
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    File URL: https://researchonline.lse.ac.uk/id/eprint/128366/
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    References listed on IDEAS

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    1. Damien Lamberton & Mohammed Mikou, 2008. "The critical price for the American put in an exponential Lévy model," Finance and Stochastics, Springer, vol. 12(4), pages 561-581, October.
    2. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    3. Baurdoux, Erik J. & Pedraza, José M., 2024. "Lp optimal prediction of the last zero of a spectrally negative Lévy process," LSE Research Online Documents on Economics 119468, London School of Economics and Political Science, LSE Library.
    4. Kristoffer Glover & Hardy Hulley, 2014. "Optimal prediction of the last-passage time of a transient diffusion," Published Paper Series 2014-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Gustavo Manso & Bruno Strulovici & Alexei Tchistyi, 2010. "Performance-Sensitive Debt," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 1819-1854.
    6. John K.-H. Quah & Bruno Strulovici, 2013. "Discounting, Values, and Decisions," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 896-939.
    7. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
    8. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    9. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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