Optimal Dividends Under Erlang(2) Inter-Dividend Decision Times

Abstract

In the classical dividends problem, dividend decisions are allowed to be made at any time. Under such a framework, the optimal dividend strategies are often of barrier or threshold type, which can lead to very irregular dividend payments over time. In practice however companies distribute dividends on a periodic basis. In that spirit, Erlangisation techniques have been used to approximate problems with fixed inter-dividend decision times. When studying the optimality of such strategies, the existing literature focuses exclusively on the special case of exponential - that is, Erlang(1) - inter-dividend decision times. Higher dimensional models are surprisingly difficult to study due to the implicit nature of some of the equations. While some of this difficulty continues to exist in high dimensions, in this paper we provide a stepping stone to the general Erlang(n) problem by providing a detailed analysis of the optimality of periodic barrier strategies when inter-dividend-decision times are Erlang(2) distributed. Results are illustrated.