Optimal dividend problem for a generalized compound Poisson risk model

TL;DR

This paper investigates the optimal dividend distribution strategy for a company with a surplus modeled by a generalized compound Poisson process, including classical and Polya-Aeppli models, showing barrier strategies are optimal under certain conditions.

Contribution

It extends the optimal dividend problem to a generalized Poisson risk model, demonstrating the optimality of barrier strategies in this broader setting.

Findings

Barrier strategies are optimal under certain conditions.

The model includes classical and Polya-Aeppli risk models as special cases.

Optimal dividend policy maximizes expected discounted dividends.

Abstract

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model including the classical risk model and the Polya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy.