A unified treatment of dividend payment problems under fixed cost and implementation delays |
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Authors: | Erhan Bayraktar Masahiko Egami |
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Institution: | 1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA 2. Graduate School of Economics, Kyoto University, Sakyo-Ku, Kyoto, 606-8501, Japan
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Abstract: | In this paper we study the dividend optimization problem for a corporation or a financial institution when the management
faces (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting
processes, Ornstein–Uhlenbeck and square-root processes. Since the cash flow structure of different companies have different
qualitative behaviors, it makes sense to use different diffusions to model them. The delay causes significant difficulties
to the optimization problem since the cash reservoir fluctuates during the delay period. We provide a uniform mathematical
framework to analyze all the models and provide optimal threshold strategies at which the management initiates actions, i.e.,
declaration and payment of dividends. Our solution depends on a new characterization of the value function for one-dimensional
diffusions and provide easily implementable algorithms to find the optimal control and the value function. |
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Keywords: | |
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