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.

摘要

在谱负 Lévy 风险模型中，我们研究了具有一般贴现函数的绝对连续股息问题，这导致了时间不一致的控制问题。在破产时间值和指数时间范围的假设下，研究了破产前贴现预期红利组成的收益函数在博弈论框架内的均衡红利策略。利用扩展的Hamilton-Jacobi-Bellman方程组技术，我们证明了验证定理并给出了返回函数的性质。对于指数贴现函数的混合，我们在 Cramér-Lundberg 模型及其扩散近似中获得了封闭形式的均衡股息策略和相应的均衡价值函数。此外，