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Mathematical Problems in Engineering
Volume 2017, Article ID 5285690, 15 pages
Research Article

The Optimal Dividend Payout Model with Terminal Values and Its Application

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China
2School of Mathematics, Yibin University, Yibin, Sichuan 644007, China

Correspondence should be addressed to Xiankang Luo; moc.361@8791oulkx

Received 4 August 2017; Accepted 31 October 2017; Published 12 December 2017

Academic Editor: Quanxin Zhu

Copyright © 2017 Xiankang Luo et al. 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.


For some firms with large nonliquid assets, preferred shareholders can still get back a little bit of money when the firms finish disbursement of loans at the status of bankruptcy. For such a situation, to investigate the optimal dividend policy, a stochastic dynamic dividend model with nonzero terminal bankruptcy values is put forward in this paper. Moreover, an analytic solution for the optimal objective function of the discounted dividends is provided and verified. An important application of this result is that it can be employed to construct the solution for the optimal value function on the dividend problem with bailouts at bankruptcy. Further, the relationship for the solutions of these two different problems is demonstrated. In the end, some numerical examples are provided to support our theoretical results and the corresponding economic interpretations are illustrated.