Tax optimization with a terminal value for the Lévy risk processes

In this paper, the surplus process (before taxes are deducted) for an insurance company evolves as a spectrally negative Lévy with usual exclusion of subordinator or deterministic drift. Tax payments collected according to very general loss-carry-forward tax system introduced in [20]. We consider optimal problem taking into account both expected discounted and time value ruin. The function strategy derived, some numerical examples also provided.