We study the rough asymptotic behaviour of a general economic risk model in adiscrete setting. Both financial and insurance risks are taken into account.Loss during the first $n$ years is modelled as a random variable$B_1+A_1B_2+\ldots+A_1\ldots A_{n-1}B_n$, where $A_i$ corresponds to thefinancial risk of the year $i$ and $B_i$ represents the insurance riskrespectively. Risks of the same year $i$ are not assumed to be independent. The main result shows that ruin probabilities exhibit power law decay undergeneral assumptions. Our objective is to give a complete characterisation ofthe relevant quantities that describe the speed at which the ruin probabilityvanishes as the amount of initial capital grows. These quantities can beexpressed as maximal moments, called moment indices, of suitable randomvariables. In addition to the study of ultimate ruin, the case of finite timeinterval ruin is considered. Both of these investigations make extensive use ofthe new properties of moment indices developed during the first half of thepaper.
展开▼
机译：我们研究了离散环境下一般经济风险模型的粗糙渐近行为。金融和保险风险均被考虑在内。前$ n $年的亏损被建模为随机变量$ B_1 + A_1B_2 + \ ldots + A_1 \ ldots A_ {n-1} B_n $，其中$ A_i $对应于金融年风险$ i $和$ B_i $分别代表保险风险。假定同年$ i $的风险是独立的。主要结果表明，在一般假设下，破产概率表现出幂律衰减。我们的目标是对相关数量进行完整的描述，以描述随着初始资本数量的增加，破产概率消失的速度。这些量可以表示为合适的随机变量的最大矩，称为矩指数。除了研究极限破坏外，还考虑了有限时间间隔破坏的情况。这两个研究都广泛使用了本文上半部分开发的力矩指数的新特性。
展开▼
