Optimal Dividend Payout under Stochastic Discounting
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 flow of
discounted dividends until a possible insolvency time.<br /><br />
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 $r \mapsto b(r)$ 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.
2010 Mathematics Subject Classification. 91G50, 93E20, 60G40, 35R35
636
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Center for Mathematical Economics
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