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Optimal stopping of Gauss–Markov bridges

Part of: Stochastic processes Miscellaneous topics - Partial differential equations Markov processes

Published online by Cambridge University Press:  04 December 2024

Abel Azze Open the ORCID record for Abel Azze [Opens in a new window] ,
Bernardo D’Auria  and
Eduardo García-Portugués
Abel Azze*
Affiliation:
CUNEF Universidad
Bernardo D’Auria*
Affiliation:
University of Padua
Eduardo García-Portugués*
Affiliation:
Universidad Carlos III de Madrid
*
*Postal address: Department of Quantitative Methods, CUNEF Universidad, Spain. Email address: [email protected]
**Postal address: Department of Mathematics, University of Padua, Italy. Email address: [email protected]
***Postal address: Department of Statistics, Universidad Carlos III de Madrid, Spain. Email address: [email protected]
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Abstract

We solve the non-discounted, finite-horizon optimal stopping problem of a Gauss–Markov bridge by using a time-space transformation approach. The associated optimal stopping boundary is proved to be Lipschitz continuous on any closed interval that excludes the horizon, and it is characterized by the unique solution of an integral equation. A Picard iteration algorithm is discussed and implemented to exemplify the numerical computation and geometry of the optimal stopping boundary for some illustrative cases.

Keywords

Optimal stoppingOrnstein–Uhlenbeck bridgetime-inhomogeneity

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 35R35: Free boundary problems
Secondary: 60J60: Diffusion processes 60G15: Gaussian processes
Type
Original Article
Information
Advances in Applied Probability , Volume 57 , Issue 1 , March 2025 , pp. 1 - 34
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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