论文标题
Gerber-Shiu折扣罚款功能：从实际角度来看
The Gerber-Shiu discounted penalty function: A review from practical perspectives
论文作者
论文摘要
Gerber-Shiu功能为评估各种风险量的统一框架提供了一个统一的框架。自成立以来，它一直吸引着对精算科学的不断提高的兴趣，而传统研究一直集中在寻找分析或半分析解决方案上，除了对相当简单的风险模型的罚款功能有限。与它的一般性相反，Gerber-Shiu功能在实践中似乎不够普遍，这在很大程度上是由于数值近似和统计推断的各种困难。为了增强有关此类实施方面的研究活动，我们对现有配方和潜在的盈余过程进行了全面的审查，以及对Gerber-Shiu功能的分析，半分析和渐近方法进行的广泛调查，该方法完全对其数值方法和统计学推进为进一步发展提供了新的光线。根据雄心勃勃的235篇参考，本调查也可以作为实用角度的模型和方法选择的有见地的指南。
The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research has been focused on finding analytical or semi-analytical solutions, either of which is rarely available, except for limited classes of penalty functions on rather simple risk models. In contrast to its great generality, the Gerber-Shiu function does not seem sufficiently prevalent in practice, largely due to a variety of difficulties in numerical approximation and statistical inference. To enhance research activities on such implementation aspects, we provide a comprehensive review of existing formulations and underlying surplus processes, as well as an extensive survey of analytical, semi-analytical and asymptotic methods for the Gerber-Shiu function, which altogether shed fresh light on its numerical methods and statistical inference for further developments. On the basis of an ambitious collection of 235 references, the present survey can serve as an insightful guidebook to model and method selection from practical perspectives as well.
