Speaker: Bahman Angoshtari (University of Washington)
Title: Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates
We consider the optimal dividend problem under a habit formation constraint that prevents the dividend rate to fall below a certain proportion of its historical maximum, the so-called drawdown constraint. This is a generalization of the optimal Duesenberry's ratcheting consumption problem, studied by Dybvig [Review of Economic Studies (1995), 62, 287--313], where consumption is assumed to be nondecreasing. The problem is formulated as a stochastic control problem with the objective of maximizing the expected discounted utility of the dividend stream until bankruptcy. The corresponding HJB equation takes the form of a nonlinear double free boundary problem, and is solved in closed form - up to the solution of an algebraic equation. The optimal excess dividend rate c(t) - as a function of the company's current surplus X(t) and the historical running maximum of dividend rates z(t) - is as follows. There are constants 0< k1 < k2, such that: (1) for 0 < X(t) < k1 * z(t), it is optimal to pay dividend at the lowest rate allowed by the drawdown constraint; (2) for k1 * z(t) < X(t) < k2 * z(t), it is optimal to distribute dividend at an intermediate level higher that the lowest rate, but not more than the historical peak z(t); and
(3) for X(t) > k2 * z(t), it is optimal to increase the dividend rate beyond its historical peak.
This is joint work with Erhan Bayraktar and Virginia Young.