Table of Contents
Chinese Journal of Mathematics
Volume 2017, Article ID 3596037, 10 pages
https://doi.org/10.1155/2017/3596037
Research Article

Value Function and Optimal Rule on the Optimal Stopping Problem for Continuous-Time Markov Processes

College of Economics and Management and Zhejiang Provincial Research, Center for Ecological Civilization, Zhejiang Sci-Tech University, Hangzhou 310018, China

Correspondence should be addressed to Lu Ye; moc.liamtoh@lyjazwjz

Received 30 May 2017; Accepted 5 September 2017; Published 9 October 2017

Academic Editor: Antonio Di Crescenzo

Copyright © 2017 Lu Ye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers the optimal stopping problem for continuous-time Markov processes. We describe the methodology and solve the optimal stopping problem for a broad class of reward functions. Moreover, we illustrate the outcomes by some typical Markov processes including diffusion and Lévy processes with jumps. For each of the processes, the explicit formula for value function and optimal stopping time is derived. Furthermore, we relate the derived optimal rules to some other optimal problems.