Optimal dividend distribution under Markov-regime switching
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0812.4978.
Date of creation: Dec 2008
Date of revision: Apr 2011
Contact details of provider:
Web page: http://arxiv.org/
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bjarne Højgaard & Michael Taksar, 2001. "Optimal risk control for a large corporation in the presence of returns on investments," Finance and Stochastics, Springer, vol. 5(4), pages 527-547.
- Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.
- Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
- Xin Guo & Jianjun Miao & Erwan Morellec, 2002.
"Irreversible Investment with Regime Shifts,"
FAME Research Paper Series
rp99, International Center for Financial Asset Management and Engineering.
- Radner, Roy & Shepp, Larry, 1996. "Risk vs. profit potential: A model for corporate strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 20(8), pages 1373-1393, August.
- Zhengjun Jiang & Martijn Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Finance and Stochastics, Springer, vol. 12(3), pages 331-355, July.
- John Driffill & Turalay Kenc & Martin Sola, 2002. "Merton-style option pricing under regime switching," Computing in Economics and Finance 2002 304, Society for Computational Economics.
- Bauerle, Nicole, 1996. "Some results about the expected ruin time in Markov-modulated risk models," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 119-127, July.
- Løkka, Arne & Zervos, Mihail, 2008. "Optimal dividend and issuance of equity policies in the presence of proportional costs," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 954-961, June.
- Ravi Bansal & Hao Zhou, 2002.
"Term Structure of Interest Rates with Regime Shifts,"
Journal of Finance,
American Finance Association, vol. 57(5), pages 1997-2043, October.
- Ravi Bansal & Hao Zhou, 2001. "Term structure of interest rates with regime shifts," Finance and Economics Discussion Series 2001-46, Board of Governors of the Federal Reserve System (U.S.).
- Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-84, December.
- Massimo Guidolin & Allan Timmerman, 2005. "Optimal portfolio choice under regime switching, skew and kurtosis preferences," Working Papers 2005-006, Federal Reserve Bank of St. Louis.
- Zhu, Jinxia & Yang, Hailiang, 2008. "Ruin theory for a Markov regime-switching model under a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 311-318, February.
- Robert J. Elliott & John van der Hoek, 1997. "An application of hidden Markov models to asset allocation problems (*)," Finance and Stochastics, Springer, vol. 1(3), pages 229-238.
- Z. Jiang & M. R. Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Papers 0803.2302, arXiv.org.
- Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.