Optimal dividends in the dual model under transaction costs

TL;DR

This paper investigates the optimal dividend payment strategy for spectrally positive Lévy processes under constant transaction costs, establishing a threshold-based policy and analyzing its properties through analytical and numerical methods.

Contribution

It introduces a $(c_1,c_2)$-policy for dividend payments in the dual model with transaction costs, extending previous models to a broader class of Lévy processes.

Findings

Optimal strategy is a $(c_1,c_2)$-policy based on surplus thresholds.

Value function expressed via scale functions.

Numerical results confirm analytical findings and convergence to no-transaction case.

Abstract

We analyze the optimal dividend payment problem in the dual model under constant transaction costs. We show, for a general spectrally positive L\'{e}vy process, an optimal strategy is given by a $(c_1,c_2)$-policy that brings the surplus process down to $c_1$ whenever it reaches or exceeds $c_2$ for some $0 \leq c_1 < c_2$. The value function is succinctly expressed in terms of the scale function. A series of numerical examples are provided to confirm the analytical results and to demonstrate the convergence to the no-transaction cost case, which was recently solved by Bayraktar et al. (2013).