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Optimal loss-carry-forward taxation for Lévy risk processes stopped at general draw-down time

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  03 September 2019

Wenyuan Wang  and
Zhimin Zhang
Wenyuan Wang*
Affiliation:
Xiamen University
Zhimin Zhang*
Affiliation:
Chongqing University
*
* Postal address: School of Mathematical Sciences, Xiamen University, Fujian 361005, P. R. China. Email address: wwywang@xmu.edu.cn
** Postal address: College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P. R. China. Email address: zmzhang@cqu.edu.cn
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Abstract

Motivated by Avram, Vu and Zhou (2017), Kyprianou and Zhou (2009), Li, Vu and Zhou (2017), Wang and Hu (2012), and Wang and Zhou (2018), 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 (2009). 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.

Keywords

Spectrally negative Lévy processdraw-down timeHamilton–Jacobi–Bellman equationtax optimization

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 93E20: Optimal stochastic control
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 3 , September 2019 , pp. 865 - 897
Copyright
© Applied Probability Trust 2019 

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