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Article Dans Une Revue Stochastic Models Année : 2022

First passage time density of an Ornstein-Uhlenbeck process with broken drift

Résumé

We consider an Ornstein-Uhlenbeck process with different drift rates below and above zero. We derive an analytic expression for the density of the first time, where the process hits a given level. The passage time density is linked to the joint law of the process and its running supremum, and we also provide an analytic formula of the joint density / distribution function. Results from a numerical experiment reveal that our formulas allow to numerically evaluate the joint law and the density of the first passage time faster than a simulation based method.
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Dates et versions

hal-03159498 , version 1 (04-03-2021)

Identifiants

Citer

Stefan Ankirchner, Christophette Blanchet-Scalliet, Diana Dorobantu, Laura Gay. First passage time density of an Ornstein-Uhlenbeck process with broken drift. Stochastic Models, 2022, 38 (2), pp.308-329. ⟨10.1080/15326349.2022.2026790⟩. ⟨hal-03159498⟩
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