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Article Dans Une Revue Advances in Applied Probability Année : 2002

Excursions height- and length-related stopping times, and application to finance

Laurent Gauthier

Résumé

In this paper, we study the first instant when Brownian motion either spends consecutively more than a certain time above a certain level, or reaches another level. This stopping time generalizes the ‘Parisian’ stopping times that were introduced by Chesney et al. (1997). Using excursion theory, we derive the Laplace transform of this stopping time. We apply this result to the valuation of investment projects with a delay constraint, but with an alternative: pay a higher cost and get the project started immediately
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Dates et versions

hal-04328825 , version 1 (07-12-2023)

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Laurent Gauthier. Excursions height- and length-related stopping times, and application to finance. Advances in Applied Probability, 2002, 34 (4), pp.846-868. ⟨10.1239/aap/1037990956⟩. ⟨hal-04328825⟩
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