A note on the optimal dividends problem with transaction costs in a spectrally negative L\'evy model with Parisian ruin

TL;DR

This paper demonstrates that an (a,b)-strategy optimally maximizes dividend payments with fixed transaction costs in a spectrally negative Lévy model with Parisian ruin, under certain tail conditions of the Lévy measure.

Contribution

It extends the optimal dividend problem to include Parisian ruin and fixed transaction costs, identifying conditions for the optimal (a,b)-strategy.

Findings

(a,b)-strategy is optimal under log-convex Lévy tail.

Results generalize previous models without Parisian ruin.

Provides conditions for optimal dividend distribution in complex Lévy models.

Abstract

In this note, merging ideas from Loeffen (2009) and Renaud (2019), we prove that an (a,b)-strategy maximizes dividend payments subject to fixed transaction costs in a spectrally negative L\'evy model with Parisian ruin, as long as the tail of the L\'evy measure is log-convex.