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Optimal loss-carry-forward taxation for Lévy risk processes stopped at general draw-down time. (English) Zbl 1427.60084

Summary: Motivated by F. Avram et al. [Insur. Math. Econ. 76, 69–74 (2017; Zbl 1395.91245)], A. E. Kyprianou and X. Zhou [J. Appl. Probab. 46, No. 4, 1146–1156 (2009; Zbl 1210.60098)], B. Li et al. [ibid. 56, No. 2, 441–457 (2019; Zbl 1415.60048)], the first author and Y. Hu [Insur. Math. Econ. 50, No. 1, 121–130 (2012; Zbl 1238.91086)], and the first author and X. Zhou [J. Appl. Probab. 55, No. 2, 513–542 (2018; Zbl 1396.91314)], we consider in this paper the problem of maximizing the expected accumulated discounted tax payments of an insurance company, whose reserve process (before taxes are deducted) 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 [Kyprianou and Zhou, loc. cit.]. To achieve a balance between taxation optimization and solvency, we consider an interesting modified objective function by considering the expected accumulated discounted tax payments of the company until the general draw-down time, instead of until the classical ruin time. The optimal tax return function and the optimal tax strategy are derived, and some numerical examples are also provided.

MSC:

60G51 Processes with independent increments; Lévy processes
91B05 Risk models (general)
93E20 Optimal stochastic control
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