Mixed Periodic-classical barrier strategies for Lévy risk processes

Abstract

Given a spectrally negative Lévy process and independent Poisson observation times, we consider a periodic barrier strategy that pushes the process down to a certain level whenever it is above it. We also consider the versions with additional classical reflection above and/or below. Using scale functions and excursion theory, various fluctuation identities are computed in terms of the scale function. Applications in de Finetti's dividend problems are also discussed.

References in corpus (3)

• On the optimal dividend problem for a spectrally negative Lévy process
• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes
• Exit identities for Lévy processes observed at Poisson arrival times

Cited by in corpus (3)

• The $W,Z$ scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends
• On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models
• American options under periodic exercise opportunities