Equilibrium dividend strategies for spectrally negative Lévy processes with time value of ruin and random time horizon

Yongxia Zhao, Hua Dong and Wei Zhong

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 14, 4757-4780

Abstract: In the spectrally negative Lévy risk model, we investigate the absolutely continuous dividend problem with a general discount function, which results in a time-inconsistent control problem. Under the assumptions of a time value of ruin and an exponential time horizon, we study the equilibrium dividend strategies within a game theoretic framework for the return function composed by the discount expected dividend before the ruin. Using the technique of extended Hamilton-Jacobi-Bellman system of equations, we show the verification theorem and give the property of return function. For a mixture of exponential discount function, we obtain closed-form equilibrium dividend strategies and the corresponding equilibrium value functions in both a Cramér–Lundberg model and its diffusion approximation. In addition, some numerical examples are presented to discuss the impacts of some parameters on the control problem.

Date: 2022
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DOI: 10.1080/03610926.2020.1822407

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