Classical, Singular, and Impulse Stochastic Control for the Optimal Dividend Policy when There is Regime Switching

Motivated by economic and empirical arguments, we consider a company whose cash reservoir is affected by macroeconomic conditions. Specifically, we model the cash reservoir as a Brownian motion with drift and volatility modulated by an observable continuous-time Markov chain that represents the regime of the economy. The objective of the management is to select the dividend policy that maximizes the expected total discounted dividend payments to be received by the shareholders. We study three different cases: bounded dividend rates, unbounded dividend rates, and the case in which there are fixed costs and taxes associated to the dividend payments. These cases generate, respectively, problems of classical stochastic control with regime switching, singular stochastic control with regime switching,and stochastic impulse control with regime switching (a new problem in the stochastic control literature). We solve these problems, and obtain the first analytical solutions for the optimal dividend policy in the presence of business cycles. Our results shows, among other things, that the optimal dividend policy depends strongly on macroeconomic conditions