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XIII Symposium on Probability and Stochastic ProcessesPredicting the Last Zero of a Spectrally Negative Lévy Process

XIII Symposium on Probability and Stochastic Processes: Predicting the Last Zero of a Spectrally... [Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the problem of finding a stopping time that minimises the L1-distance to the last time a spectrally negative Lévy process X is below zero. Examples of related problems in a finite horizon setting for processes with continuous paths are by Du Toit et al. (Stochastics Int J Probab Stochastics Process 80(2–3):229–245, 2008) and Glover and Hulley (SIAM J Control Optim 52(6):3833–3853, 2014), where the last zero is predicted for a Brownian motion with drift, and for a transient diffusion, respectively.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

XIII Symposium on Probability and Stochastic ProcessesPredicting the Last Zero of a Spectrally Negative Lévy Process

Part of the Progress in Probability Book Series (volume 75)
Editors: López, Sergio I.; Rivero, Víctor M.; Rocha-Arteaga, Alfonso; Siri-Jégousse, Arno
Baurdoux, Erik J.; Pedraza, José M.
XIII Symposium on Probability and Stochastic Processes — Oct 17, 2020
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References (23)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
ISBN
978-3-030-57512-0
Pages
77 –105
DOI
10.1007/978-3-030-57513-7_4
Publisher site
See Chapter on Publisher Site

Abstract

[Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the problem of finding a stopping time that minimises the L1-distance to the last time a spectrally negative Lévy process X is below zero. Examples of related problems in a finite horizon setting for processes with continuous paths are by Du Toit et al. (Stochastics Int J Probab Stochastics Process 80(2–3):229–245, 2008) and Glover and Hulley (SIAM J Control Optim 52(6):3833–3853, 2014), where the last zero is predicted for a Brownian motion with drift, and for a transient diffusion, respectively.]

Published: Oct 17, 2020

Keywords: Lévy processes; Optimal prediction; Optimal stopping; 60G40; 62M20

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