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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 2693568, 14 pages
https://doi.org/10.1155/2017/2693568
Research Article

Classical and Impulse Stochastic Control on the Optimization of Dividends with Residual Capital at Bankruptcy

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

Correspondence should be addressed to Peimin Chen; nc.ude.efuws@nimiepnehc

Received 10 October 2016; Accepted 6 February 2017; Published 23 February 2017

Academic Editor: Yong Zhou

Copyright © 2017 Peimin Chen and Bo Li. 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

In this paper, we consider the optimization problem of dividends for the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, while accounting for the tax rate and transaction cost for dividend payout. Maximization of both expected total discounted dividends before bankruptcy and expected discounted returned money at the state of terminal bankruptcy becomes a mixed classical-impulse stochastic control problem. In order to solve this problem, we reduce it to quasi-variational inequalities with a nonzero boundary condition. We explicitly construct and verify solutions of these inequalities and present the value function together with the optimal policy.