De Angelis, T (2020) Optimal dividends with partial information and stopping of a degenerate reflecting diffusion. Finance and Stochastics, 24 (1). pp. 71-123. ISSN 0949-2984
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2019. This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | Singular control; Optimal stopping; Free boundary problems; Partial information; Dividend problem; Reflected diffusions; Stroock–Williams equation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Jun 2019 09:31 |
Last Modified: | 25 Jun 2023 21:52 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00780-019-00407-1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147375 |
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