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

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24 citations0/0 files storedAdvances in Applied Probability

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

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 Chesneyet 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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References

1994Investment Under Uncertainty.1994Investment under Uncertainty 2007Brownian Motion and Stochastic Calculus 1999Continuous Martingales and Brownian Motion 1982The Value of Waiting to Invest 1996Real Options: Managerial Flexibility and Strategy in Resource Allocation 1991Brownian motion and stochastic calculus 1991Continuous Martingales and Brownian Motion

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2009Double-sided Parisian option pricing

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