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Optimal stopping of an Ornstein-Uhlenbeck bridge

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  • D'Auria, Bernardo
  • Guada Azze, Abel

Abstract

Markov bridges may be useful models in finance to describe situations in which information on the underlying processes is known in advance. However, within the framework of optimal stopping problems, Markov bridges are inherently challenging processes as they are time-inhomogeneous and account for explosive drifts. Consequently, few results are known in the literature of optimal stopping theory related to Markov bridges, all of them confined to the simplistic Brownian bridge.In this paper we make a rigorous analysis of the existence and characterization of the free boundary related to the optimal stopping problem that maximizes the mean of an Ornstein&-Uhlenbeckbridge. The result includes the Brownian bridge problem as a limit case. The methodology hereby presented relies on a times-pace transformation that casts the original problem into a more tractable one with infinite horizon and a Brownian motion underneath. We concludeby commenting on two different numerical algorithms to compute the free-boundary equation and discuss illustrative cases that shed light on the boundary's shape. In particular,the free boundary does not generally share the monotonicity of the Brownian bridge case.

Suggested Citation

  • D'Auria, Bernardo & Guada Azze, Abel, 2021. "Optimal stopping of an Ornstein-Uhlenbeck bridge," DES - Working Papers. Statistics and Econometrics. WS 33508, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:33508
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    References listed on IDEAS

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