A Non-Stationary Model of Dividend Distribution in A Stochastic Interest-Rate Setting

In this paper the solutions to several variants of the so-called dividend-distribution problem in a multi-dimensional setting are studied. In a nutshell, the manager of a firm must balance the retention of earnings (so as to ward off bankruptcy and earn interest) and the distribution of dividends (so as to please the shareholders). A dynamic-programming approach is used, where the state variables are the current levels of cash reserves and of the stochastic short-rate, as well as time. This results in a family of Hamilton-Jacobi-Bellman variational inequalities whose solutions must be approximated numerically. To do so, a finite-element approximation and a time-marching scheme are employed