> This study addresses the issue of maximization of dividends of an insurer whose portfolio is exposed to insurance risk. The insurance risk arises from the classical surplus process commonly known as the Cramér-Lundberg model in the insurance literature. To enhance his financial base, the insurer invests in a risk free asset whose price dynamics are governed by a constant force of interest. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block method of Paulsen et al.[1] in conjunction with the Simpson rule to solve the Volterra integral equations for each chosen barrier thus generating corresponding dividend value functions. We have obtained the optimal barrier that maximizes the dividends. In the absence of the financial world, the analytical solution has been used to assess the accuracy of our results.
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机译： >这项研究解决了投资组合面临保险风险的保险公司的股利最大化问题。保险风险来自经典的盈余过程，在保险文献中通常被称为Cramér-Lundberg模型。为了增强其财务基础，保险公司投资了无风险资产，其价格动态受恒定的利率影响。我们推导第二类线性Volterra积分方程，并结合Simpson规则应用Paulsen et al 。 [1] 的四阶逐块方法为每个选定的障碍求解Volterra积分方程，从而生成相应的红利值函数。我们已经获得了使红利最大化的最佳壁垒。在没有金融世界的情况下，分析解决方案已用于评估我们结果的准确性。
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