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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 971212, 15 pages
http://dx.doi.org/10.1155/2012/971212
Research Article

The First Passage Time and the Dividend Value Function for One-Dimensional Diffusion Processes between Two Reflecting Barriers

1School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China
2School of Economics and Management, Southeast University, Nanjing 211189, China

Received 26 July 2012; Accepted 24 September 2012

Academic Editor: Enzo Orsingher

Copyright © 2012 Chuancun Yin and Huiqing Wang. 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

We consider the general one-dimensional time-homogeneous regular diffusion process between two reflecting barriers. An approach based on the Itô formula with corresponding boundary conditions allows us to derive the differential equations with boundary conditions for the Laplace transform of the first passage time and the value function. As examples, the explicit solutions of them for several popular diffusions are obtained. In addition, some applications to risk theory are considered.