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Journal of Applied Mathematics
Volume 2014, Article ID 184098, 7 pages
Research Article

Dividend Problems with a Barrier Strategy in the Dual Risk Model until Bankruptcy

1Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
2Department of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China

Received 29 March 2014; Revised 19 July 2014; Accepted 21 July 2014; Published 11 August 2014

Academic Editor: Daqing Jiang

Copyright © 2014 Donghai Liu and Zaiming Liu. 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.


The paper studies the dual risk model with a barrier strategy under the concept of bankruptcy, in which one has a positive probability to continue business despite temporary negative surplus. Integrodifferential equations for the expectation of the discounted dividend payments and the probability of bankruptcy are derived. Moreover, when the gain size distribution is exponential, explicit solutions for the expected dividend payments and the bankruptcy probability are obtained for constant bankruptcy rate function. It also provided some numerical examples to illustrate the applications of the explicit solutions.