SIAM Journal on Financial Mathematics, Volume 12, Issue 1, Page 29-46, January 2021.
We revisit the classical problem of optimal payment of dividends and determine the degree to which the diffusion approximation serves as a valid approximation of the classical risk model for this problem. Our results parallel some of those in Bäuerle [Math. Finance, 14 (2004), pp. 99--113], but we obtain sharper results because we use a different technique for obtaining them. Specifically, Bäuerle uses probabilistic techniques and relies on convergence in distribution of the underlying processes. By contrast, we use comparison results from the theory of differential equations, and these methods allow us to determine the rate of convergence of the value functions in question.

中文翻译：

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最优股息问题：渐近分析

SIAM Journal on Financial Mathematics，第 12 卷，第 1 期，第 29-46 页，2021 年 1 月。
我们重新审视最优股息支付的经典问题，并确定扩散近似作为经典风险模型的有效近似的程度这个问题。我们的结果与 Bäuerle [Math. Finance, 14 (2004), pp. 99--113]，但我们获得了更清晰的结果，因为我们使用了不同的技术来获得它们。具体来说，Bäuerle 使用概率技术并依赖于底层过程分布的收敛。相比之下，我们使用微分方程理论的比较结果，这些方法使我们能够确定所讨论的价值函数的收敛速度。