Optimal dividend distribution under Markov-regime switching
File(s)
Published version
Author(s)
Jiang, Z
Pistorius, M
Type
Journal Article
Abstract
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.
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.
Date Issued
2012-03-02
Citation
Finance and Stochastics, 2012, 16 (3), pp.449-476
ISSN
0949-2984
Publisher
Springer
Start Page
449
End Page
476
Journal / Book Title
Finance and Stochastics
Volume
16
Issue
3
Copyright Statement
© The Author(s) 2012. This article is published with open access at Springerlink.com. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
http://arxiv.org/abs/0812.4978v2
Publication Status
Published