Optimal dividend and capital injection strategy with fixed costs and restricted dividend rate for a dual model

Dingjun Yao; Rongming Wang; Lin Xu

doi:10.3934/jimo.2014.10.1235

Article Contents

2014, Volume 10, Issue 4: 1235-1259. Doi: 10.3934/jimo.2014.10.1235

This issue Previous Article Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem Next Article Optimal pricing policy for deteriorating items with preservation technology investment

Optimal dividend and capital injection strategy with fixed costs and restricted dividend rate for a dual model

1.
School of Finance, The Center of Cooperative Innovation for Modern Service Industry, Nanjing University of Finance and Economics, Nanjing 210023
2.
School of Finance and Statistics, Research Center of International Finance and Risk Management, East China Normal University, Shanghai 200241
3.
School of Mathematics and Computer Sciences, Anhui Normal University, Wuhu, Anhui, 241003

Received: April 2013

Revised: October 2013

Published: October 2014

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Abstract

In the framework of dual risk model, Yao et al. [18](Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs. European Journal of Operational Research, 211, 568-576) show how to determine optimal dividend and capital injection strategy when the dividend rate is unrestricted and the bankruptcy is forbidden. In this paper, we further include constrain on dividend rate and allow for bankruptcy when it is in deficit. We seek the optimal strategy for maximizing the expected discounted dividends minus the discounted capital injections before bankruptcy. Explicit solutions for strategy and value function are obtained when income jumps follow a hyper-exponential distribution, the corresponding limit results are presented, some known results are extended.

Keywords:

Mathematics Subject Classification: Primary: 93E20, 91G50; Secondary: 91G80.

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