In this paper we investigate the problem of optimal dividend distribution  in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a drifted Brownian motion modulated by a finite state Markov chain, and model the discount rate as a deterministic function of the current state of the chain. The objective is to maximize the expected cumulative discounted dividend payments until the moment of bankruptcy, which occurs the first time that the cash reserves (the cumulative net revenues minus cumulative dividend payments) hit zero. We show that, if the drift is positive in each regime , it is optimal to adopt a barrier strategy at certain positive regime-dependent levels, and explicitly characterize the value function as the fixed point of a contraction. In the case that the drift is small and negative in some regime , the optimal strategy takes a different form, which we explicitly identify in the case that there are two regimes. We also provide a numerical illustration of the sensitivities of the optimal barriers and the influence of regime-switching.
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a deterministic function of the current state of the chain. In this setting the objective of the company is to maximize the expected cumulative discounted dividend payments until the moment of bankruptcy, which is taken to be the first time that the cash reserves (the cumulative net revenues minus cumulative dividend payments) are zero. We show that, if the drift is positive in each state , it is optimal to adopt a barrier strategy at certain positive regime-dependent levels, and provide an explicit characterization of the value function as the fixed point of a contraction. In the case that the drift is small and negative in one state , the optimal strategy takes a different form, which we explicitly identify if there are two regimes. We also provide a numerical illustration of the sensitivities of the optimal barriers and the influence of regime-switching.
R
In this paper we
We
A
for a company
R
drifted Brownian motion
Brownian motion with positive drift that is
R
The objective
In this setting the objective of the company
R
occurs
is taken to be
R
hit
are
R
regime
state
R
explicitly characterize
provide an explicit characterization of
R
some regime
one state
R
in the case that
if