论文标题
随机损失的参数分解性
Parametric divisibility of stochastic losses
论文作者
论文摘要
如果存在其n卷积根，则概率分布是N分布的。虽然通过增添风险因素模型对几个（重新）保险损失之间的依赖结构进行建模，但无限的可划分性，这是所有$ n \ in \ mathbb n $中的$ n $ didiblesible，这是一个非常可取的属性。此外，还需要计算零件分布（即卷积根）的能力。不幸的是，如果许多有用的分布都是无限的分配，那么计算其零件的分布通常是一项具有挑战性的任务，需要大量的数值计算。但是，在少数选定的情况下，尤其是伽马案例，可以完全参数地进行零件分布的提取，即具有可忽略的数值成本和零误差。我们展示了如何利用伽马分布的整洁属性来近似其他分布的部分，并提供了所得算法的几个插图。
A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the $n$-divisibility for all $n \in\mathbb N$, is a very desirable property. Moreover, the capacity to compute the distribution of a piece (i.e., a convolution root) is also desirable. Unfortunately, if many useful distributions are infinitely divisible, computing the distributions of their pieces is usually a challenging task that requires heavy numerical computations. However, in a few selected cases, particularly the Gamma case, the extraction of the distribution of the pieces can be performed fully parametrically, that is with negligible numerical cost and zero error. We show how this neat property of Gamma distributions can be leveraged to approximate the pieces of other distributions, and we provide several illustrations of the resulting algorithms.
