Mathematical Methods of Operations Research

, Volume 71, Issue 2, pp 325–351

A unified treatment of dividend payment problems under fixed cost and implementation delays

Original Article
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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.

Keywords

Impulse control Implementation delay Dividend payments Brownian motion Ornstein–Uhlenbeck process Square-root process Itô diffusions 

Mathematics Subject Classification (2000)

Primary: 93E20 Secondary: 60J60 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Graduate School of EconomicsKyoto UniversitySakyo-Ku, KyotoJapan

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