Spectrally negative Lévy processes with Parisian reflection below and classical reflection above

Abstract

We consider a company that receives capital injections so as to avoid ruin. Differently from the classical bail-out settings where the underlying process is restricted to stay at or above zero, we study the case bail-out can only be made at independent Poisson times. Namely, we study a version of the reflected process that is pushed up to zero only on Poisson observation times at which the process is below zero. We also study the case with additional classical reflection above so as to model a company that pays dividends according to a barrier strategy. Focusing on the spectrally negative Lévy case, we compute, using the scale function, various fluctuation identities including capital injections and dividends.

References in corpus (3)

• On the optimal dividend problem for a spectrally negative Lévy process
• On the Refracted-Reflected Spectrally Negative Lévy Processes
• Lévy insurance risk processes with parisian type severity of debt

Cited by in corpus (4)

• On the optimality of Periodic barrier strategies for a spectrally positive Lévy process
• Generalized refracted Lévy process and its application to exit problem
• A Review of First-Passage Theory for the Segerdahl Risk Process and Extensions
• Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities