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

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.