Optimal dividends with partial information and stopping of a degenerate reflecting diffusion

Tiziano Angelis ()
Additional contact information
Tiziano Angelis: University of Leeds

Finance and Stochastics, 2020, vol. 24, issue 1, No 3, 123 pages

Abstract: Abstract We study the optimal dividend problem for a firm’s manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying process and with absorption. In the Markovian formulation, we have a two-dimensional degenerate diffusion whose first component is singularly controlled. Moreover, the process is absorbed when its first component hits zero. The free boundary problem (FBP) associated to the value function of the control problem is challenging from the analytical point of view due to the interplay of degeneracy and absorption. We find a probabilistic way to show that the value function of the dividend problem is a smooth solution of the FBP and to construct an optimal dividend strategy. Our approach establishes a new link between multidimensional singular stochastic control problems with absorption and problems of optimal stopping with ‘creation’. One key feature of the stopping problem is that creation occurs at a state-dependent rate of the ‘local time’ of an auxiliary two-dimensional reflecting diffusion.

Keywords: Singular control; Optimal stopping; Free boundary problems; Partial information; Dividend problem; Reflected diffusions; Stroock–Williams equation; 60J70; 60G40; 91G80; 93E20 (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-019-00407-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:finsto:v:24:y:2020:i:1:d:10.1007_s00780-019-00407-1

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-019-00407-1

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().