Parisian times for linear diffusions

Profeta, Christophe

doi:10.1090/tpms/1208

Author: Christophe Profeta
Journal: Theor. Probability and Math. Statist. 110 (2024), 101-119
MSC (2020): Primary 60J60, 60G40
DOI: https://doi.org/10.1090/tpms/1208
Published electronically: May 10, 2024
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Abstract: We compute the joint distribution of the first times a linear diffusion makes an excursion longer than some given duration above (resp. below) some fixed level. In the literature, such stopping times have been introduced and studied in the framework of Parisian barrier options, mainly in the case of Brownian motion with drift. We also exhibit several independence properties, and provide some formulae for the associated ruin probabilities.

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