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Journal of Applied Mathematics
Volume 2013, Article ID 467948, 7 pages
http://dx.doi.org/10.1155/2013/467948
Research Article

The Ornstein-Uhlenbeck-Type Model with a Hybrid Dividend Strategy

School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China

Received 3 August 2013; Revised 18 December 2013; Accepted 18 December 2013

Academic Editor: Mina Abd-El-Malek

Copyright © 2013 Dan Zhu and Chuancun Yin. 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 Ornstein-Uhlenbeck-type model. We first introduce the model and then find the ordinary differential equations and boundary conditions satisfied by the dividend functions; closed-form solutions for the dividend value functions are given. We also study the distribution of the time value of ruin. Furthermore, the moments and moment-generating functions of total discounted dividends until ruin are discussed.