Dividend problem with Parisian delay for a spectrally negative Lévy risk process

Abstract

In this paper we consider dividend problem for an insurance company whose risk evolves as a spectrally negative Lévy process (in the absence of dividend payments) when Parisian delay is applied. The objective function is given by the cumulative discounted dividends received until the moment of ruin when so-called barrier strategy is applied. Additionally we will consider two possibilities of delay. In the first scenario ruin happens when the surplus process stays below zero longer than fixed amount of time $\zeta >0$. In the second case there is a time lag $d$ between decision of paying dividends and its implementation.

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
• Parisian ruin probability for spectrally negative Lévy processes

Cited by in corpus (1)

• On the optimality of Periodic barrier strategies for a spectrally positive Lévy process