Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/227832
Authors: 
Bandini, Elena
De Angelis, Tiziano
Ferrari, Giorgio
Gozzi, Fausto
Year of Publication: 
2020
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 636
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 modelled by a Cox-Ingersoll-Ross (CIR) process and the firm's objective is to maximize the total expected ow 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 function r ↦ 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.
Subjects: 
Optimal dividend
stochastic interest rates
CIR model
singular control
optimal stopping
free boundary problems
JEL: 
G11
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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