EconPapers    
Economics at your fingertips  
 

Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates

Bahman Angoshtari, Erhan Bayraktar and Virginia R. Young

Papers from arXiv.org

Abstract: We consider the optimal dividend problem under a habit formation constraint that prevents the dividend rate to fall below a certain proportion of its historical maximum, the so-called drawdown constraint. This is an extension of the optimal Duesenberry's ratcheting consumption problem, studied by Dybvig (1995) [Review of Economic Studies 62(2), 287-313], in which consumption is assumed to be nondecreasing. Our problem differs from Dybvig's also in that the time of ruin could be finite in our setting, whereas ruin was impossible in Dybvig's work. We formulate our problem as a stochastic control problem with the objective of maximizing the expected discounted utility of the dividend stream until bankruptcy, in which risk preferences are embodied by power utility. We semi-explicitly solve the corresponding Hamilton-Jacobi-Bellman variational inequality, which is a nonlinear free-boundary problem. The optimal (excess) dividend rate $c^*_t$ - as a function of the company's current surplus $X_t$ and its historical running maximum of the (excess) dividend rate $z_t$ - is as follows: There are constants $0 w^* z_t$, it is optimal to increase the dividend rate above $z_t$, and (5) it is optimal to increase $z_t$ via singular control as needed to keep $X_t \le w^* z_t$. Because, the maximum (excess) dividend rate will eventually be proportional to the running maximum of the surplus, "mountains will have to move" before we increase the dividend rate beyond its historical maximum.

New Economics Papers: this item is included in nep-upt
Date: 2018-06, Revised 2019-03
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://arxiv.org/pdf/1806.07499 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1806.07499

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().

 
Page updated 2019-04-06
Handle: RePEc:arx:papers:1806.07499