We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the dividends and the penalty, which causes time-inconsistency. This allows to study different types of constraints. For the diffusion approximation of the classical surplus process we derive an explicit equilibrium dividend strategy and the associated value function. Inspired by duality arguments, we can identify a particular equilibrium strategy such that for a given initial surplus the imposed constraint is fulfilled. Furthermore, we illustrate our findings with a numerical example.

我们考虑股利最大化问题，包括扩散环境中的破产惩罚。额外的惩罚条款是由于对股息策略的限制而产生的。我们故意对股息和罚金使用不同的贴现率，这会导致时间不一致。这允许研究不同类型的约束。对于经典盈余过程的扩散近似，我们推导出明确的均衡股息策略和相关的价值函数。受对偶论点的启发，我们可以确定一种特定的均衡策略，使得对于给定的初始盈余，强加的约束得到满足。此外，我们用一个数值例子来说明我们的发现。