De Finetti's problem with fixed transaction costs and regime switching

TL;DR

This paper extends de Finetti's dividend problem by incorporating fixed transaction costs and regime switching, deriving explicit optimal strategies and analyzing the impact of financial regime changes.

Contribution

It introduces a modified surplus process with regime switching and explicitly determines the optimal two-barrier impulsive dividend strategy under these conditions.

Findings

Optimal dividend strategy is a two-barrier impulsive policy.

Explicit solutions are obtained for most regimes.

Strategy adapts to changes in drift and volatility.

Abstract

In this paper, we examine a modified version of de Finetti's optimal dividend problem, incorporating fixed transaction costs and altering the surplus process by introducing two-valued drift and two-valued volatility coefficients. This modification aims to capture the transitions or adjustments in the company's financial status. We identify the optimal dividend strategy, which maximizes the expected total net dividend payments (after accounting for transaction costs) until ruin, as a two-barrier impulsive dividend strategy. Notably, the optimal strategy can be explicitly determined for almost all scenarios involving different drifts and volatility coefficients. Our primary focus is on exploring how changes in drift and volatility coefficients influence the optimal dividend strategy.