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AN OPTIMAL DIVIDEND POLICY WITH DELAYED CAPITAL INJECTIONS

Part of: Stochastic systems and control Applications

Published online by Cambridge University Press:  18 March 2014

ZHUO JIN  and
GEORGE YIN
ZHUO JIN*
Affiliation:
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia
GEORGE YIN
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA email gyin@math.wayne.edu
*
✉zjin@unimelb.edu.au
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Abstract

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This work focuses on finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections with delays. Starting from the classical Cramér–Lundberg process, using the dynamic programming approach, the value function obeys a quasi-variational inequality. With delays in capital injections, the company will be exposed to the risk of financial ruin during the delay period. In addition, the optimal dividend payment and capital injection strategy should balance the expected cost of the possible capital injections and the time value of the delay period. In this paper, the closed-form solution of the value function and the corresponding optimal policies are obtained. Some limiting cases are also discussed. A numerical example is presented to illustrate properties of the solution. Some economic insights are also given.

Keywords

capital injectiondelaydividend policysingular control

MSC classification

Secondary: 93E20: Optimal stochastic control 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 2 , October 2013 , pp. 129 - 150
Copyright
Copyright © 2014 Australian Mathematical Society 

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