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

Part of: Mathematical economics Markov processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Laurent Gauthier
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Abstract

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

Keywords

Parisian optionsBrownian excursionsreal options

MSC classification

Primary: 60J65: Brownian motion 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 91B06: Decision theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 4 , December 2002 , pp. 846 - 868
Copyright
Copyright © Applied Probability Trust 2002 

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