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Teor. Veroyatnost. i Primenen., 2020, Volume 65, Issue 3, Pages 437–459 (Mi tvp5205)  

Optimality of threshold stopping times for diffusion processes

V. I. Arkin

Central Economics and Mathematics Institute Russian Academy of Sciences, Moscow

Abstract: This paper is concerned with the optimal stopping problem for Itô diffusion processes over a class of stopping times. Necessary and sufficient optimality conditions are studied for a parametrically specified class of stopping times. A detailed analysis is given for the case of one-dimensional diffusion processes and threshold stopping times. Necessary and sufficient conditions are put forward for optimality of a threshold stopping time over all stopping times. A number of relations are obtained between the solution of the optimal stopping problem over the class of threshold moments and the solution of the free-boundary problem.

Keywords: diffusion processes, optimal stopping, threshold stopping time, free-boundary problem.

DOI: https://doi.org/10.4213/tvp5205

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English version:
Theory of Probability and its Applications, 2020, 65:3, 341–358

Bibliographic databases:

Received: 17.01.2018
Revised: 28.06.2019
Accepted:11.07.2019

Citation: V. I. Arkin, “Optimality of threshold stopping times for diffusion processes”, Teor. Veroyatnost. i Primenen., 65:3 (2020), 437–459; Theory Probab. Appl., 65:3 (2020), 341–358

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