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 process with the usual exclusion of negative subordinator or deterministic drift. Tax payments are collected according to the very general loss-carry-forward tax system introduced in [20]. We consider an optimal tax problem taking into account both the expected discounted tax payments and the time value of ruin. The optimal tax value function and the optimal tax strategy are derived, some numerical examples are also provided.