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OPTIMAL FINANCING AND DIVIDEND DISTRIBUTION WITH TRANSACTION COSTS IN THE CASE OF RESTRICTED DIVIDEND RATES

Published online by Cambridge University Press:  05 October 2016

Jinxia Zhu
Jinxia Zhu*
Affiliation:
School of Risk and Actuarial Studies, UNSW Business School, The University of New South Wales, Sydney, NSW 2031, Australia
*
E-Mail: jinxia.zhu@unsw.edu.au
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Abstract

We consider the optimal financing (capital injections) and dividend payment problem for a Brownian motion model in the case of restricted dividend rates. The company has no obligation to inject capitals and therefore, the bankruptcy risk is present. Capital injections, if any, will incur both fixed and proportional transaction costs and dividend payments incur proportional transaction costs. The aim is to find the optimal strategy to maximize the expected present value of dividend payments minus the total cost of capital injections up to the time of bankruptcy. The problem is formulated as a mixed impulse-regular control problem. We address the problem via studying three cases of two auxiliary functions. We derive important analytical properties of the auxiliary functions and use them to study the value function and then identify the optimal control strategy. We show that the optimal dividend control is of threshold type and the optimal financing strategy prescribes to either never inject capitals or inject capitals only when the surplus reaches 0 with a fixed lump sum amount.

Keywords

Dividendfinancingtransaction costrestricted dividend ratelump sum strategy
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 1 , January 2017 , pp. 239 - 268
Copyright
Copyright © Astin Bulletin 2016 

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