On the optimality of joint periodic and extraordinary dividend strategies

TL;DR

This paper analyzes optimal dividend strategies combining periodic and extraordinary payments for a risky business modeled by Brownian motion, considering transaction costs and identifying conditions for strategy optimality.

Contribution

It introduces a comprehensive model for hybrid dividend strategies with transaction costs and characterizes the optimal strategies depending on business profitability and costs.

Findings

Hybrid strategies can be optimal under certain conditions.

Liquidation may be optimal if costs are high.

Strategy choice depends on profitability and transaction costs.

Abstract

In this paper, we model the cash surplus (or equity) of a risky business with a Brownian motion. Owners can take cash out of the surplus in the form of "dividends", subject to transaction costs. However, if the surplus hits 0 then ruin occurs and the business cannot operate any more. We consider two types of dividend distributions: (i) periodic, regular ones (that is, dividends can be paid only at countable many points in time, according to a specific arrival process); and (ii) extraordinary dividend payments that can be made immediately at any time (that is, the dividend decision time space is continuous and matches that of the surplus process). Both types of dividends attract proportional transaction costs, and extraordinary distributions also attracts fixed transaction costs, a realistic feature. A dividend strategy that involves both types of distributions (periodic and extraordinary) is qualified as "hybrid". We determine which strategies (either periodic, immediate, or hybrid) are optimal, that is, we show which are the strategies that maximise the expected present value of dividends paid until ruin, net of transaction costs. Sometimes, a liquidation strategy (which pays out all monies and stops the process) is optimal. Which strategy is optimal depends on the profitability of the business, and the level of (proportional and fixed) transaction costs. Results are illustrated.