Stochastic impulse control with regime switching for the optimal dividend policy when there are business cycles, taxes and fixed costs

Abstract

We consider the problem of finding the optimal dividend policy for a company whose cash reserve follows a Brownian motion with drift and volatility modulated by an observable finite-state continuous-time Markov chain. The Markov chain represents the regime of the economy. We allow fixed costs and taxes associated with the dividend payments. This optimization problem generates a stochastic impulse control problem with regime switching. We solve this problem and obtain the first analytical solutions for the optimal dividend policy when there are simultaneously fixed costs, taxes and business cycles. Our results show that the optimal dividend policy depends strongly on the regime of the economy, on fixed costs and on taxes.

Keywords:

• business cycles
• dividend policy
• stochastic impulse control with regime switching
• taxes

Keywords:

• 93E20
• 91B70
• 60H30

Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council of Canada grants 194137 and 194137-2010. The work of A. Cadenillas was also supported by the World Class University (WCU) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (R31-2009-000-20007). The paper is based on the PhD dissertation of L.R. Sotomayor at the University of Alberta. This paper is dedicated to the memory of Michael Taksar, who was a pioneer in the application of stochastic control methods to optimal dividend policy problems.