Optimal stopping problems with restricted stopping times

Wenqing Bao; Xianyi Wu; Xian Zhou

doi:10.3934/jimo.2016023

Article Contents

2017, Volume 13, Issue 1: 399-411. Doi: 10.3934/jimo.2016023

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Optimal stopping problems with restricted stopping times

1.
Department of Statistics and Actuarial Science, East China Normal University, Shanghai, China
2.
Department of Mathematics, Zhejiang Normal University, China
3.
Department of Applied Finance and Actuarial Studies, Macquarie University, Sydney, Australia

* Corresponding author: Prof. Xianyi Wu, E-mail: xywu@stat.ecnu.edu.cn
* Corresponding author: Prof. Xianyi Wu, E-mail: xywu@stat.ecnu.edu.cn

Received: April 30, 2015

Published: August 2017

This research was partially supported by the Natural Science Foundation of China under Grant No. 71371074, 111 Project Grant No. B14019 and the Australian Research Council Discovery Project Grant No. DP1094153.

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Abstract

This paper provides a general ground for the problems of optimal stopping times over the families of partially available (or restricted) stopping times. It subsumes the classical framework in continuous-time, discrete-time, as well as semi-Markov settings as special cases. We model the problem by a restricted pool of stopping times meeting certain natural conditions and present its solution by means of Snell's envelope technique that extends the classical results. We further extend this type of problems to the stochastic processes indexed by partially ordered set.

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Mathematics Subject Classification: Primary: 60G40; Secondary: 60G48.

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References

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