 Optimal dividend payout under stochastic discountingElena Bandini, Tiziano De Angelis, Giorgio Ferrari and Fausto Gozzi Mathematical Finance, 2022, vol. 32, issue 2, 627-677 Abstract: Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash‐flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that the problem is cast as one of singular stochastic control. The stochastic interest rate is modeled by a Cox–Ingersoll–Ross (CIR) process and the firm's objective is to maximize the total expected flow of discounted dividends until a possible insolvency time. We find an optimal dividend payout policy which is such that the surplus process is kept below an endogenously determined stochastic threshold expressed as a decreasing continuous function r↦b(r)$r\mapsto b(r)$ of the current interest rate value. We also prove that the value function of the singular control problem solves a variational inequality associated to a second‐order, non‐degenerate elliptic operator, with a gradient constraint. Date: 2022 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:32:y:2022:i:2:p:627-677 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematical Finance is currently edited by Jerome Detemple More articles in Mathematical Finance from Wiley Blackwell |
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