Get access

OPTIMAL DIVIDEND POLICY WITH MEAN-REVERTING CASH RESERVOIR

Authors


  • The work of A. Cadenillas was supported by the Social Sciences and Humanities Research Council of Canada grant 410-2003-1401. Some of his contributions were made during his visit to the Institut für Mathematik, Humboldt Universität zu Berlin, thanks to a Research Fellowship of the Humboldt Foundation. He is very grateful to Professor Hans Föllmer and the members of the Stochastics group for their very generous hospitality. The work of S. Sarkar was supported by the Social Sciences and Humanities Research Council of Canada grant 410-2005-1960. Preliminary versions of this paper have been presented at the Third World Congress of the Bachelier Finance Society (Chicago), the Quantitative Methods in Finance 2003 Conference (Sydney), and CEMFI. We are very grateful to conference and seminar participants, Chris Hennessy, the associate editor, and two anonymous referees, for many comments and suggestions. Remaining errors are our sole responsibility.

  • Manuscript received December 2003; final revision received November 2005.

Address correspondence to Fernando Zapatero, Department of Finance and Business Economics, Marshall School of Business, USC, Los Angeles, CA 90089; e-mail: fzapatero@marshall.usc.edu.

Abstract

Motivated by empirical evidence and economic arguments, we assume that the cash reservoir of a financial corporation follows a mean reverting process. The firm must decide the optimal dividend strategy, which consists of the optimal times and the optimal amounts to pay as dividends. We model this as a stochastic impulse control problem, and succeed in finding an analytical solution. We also find a formula for the expected time between dividend payments. A crucial and surprising economic result of our paper is that, as the dividend tax rate decreases, it is optimal for the shareholders to receive smaller but more frequent dividend payments. This results in a reduction of the probability of default of the firm.

Ancillary