Motivated by the EU Solvency II Directive, we study the one-year ruin probability of an insurer who makes investments and hence faces both insurance and financial risks. Over a time horizon of one year, the insurance risk is quantified as a nonnegative random variable X equal to the aggregate amount of claims, and the financial risk as a d -dimensional random vector Y consisting of stochastic discount factors of the d financial assets invested. To capture both heavy tails and asymptotic dependence of Y in an integrated manner, we assume that Y follows a standard multivariate regular variation (MRV) structure. As main results, we derive exact asymptotic estimates for the one-year ruin probability for the following cases: (i) X and Y are independent with X of Fréchet type; (ii) X and Y are independent with X of Gumbel type; (iii) X and Y jointly possess a standard MRV structure; (iv) X and Y jointly possess a nonstandard MRV structure.
展开▼
机译：受欧盟偿付能力指令II（Solvency II Directive）的影响，我们研究了进行投资并因此面临保险和金融风险的保险公司一年的破产概率。在一年的时间范围内，将保险风险量化为等于索赔总额的非负随机变量X，将金融风险量化为由所投资的d个金融资产的随机折现因子组成的d维随机向量Y。为了以集成方式捕获Y的重尾和渐近依赖性，我们假定Y遵循标准的多元正则变异（MRV）结构。作为主要结果，我们得出以下情况下一年毁灭概率的精确渐近估计：（i）X和Y与Fréchet类型的X独立; （ii）X和Y与Gumbel类型的X独立; （iii）X和Y共同拥有标准的MRV结构; （iv）X和Y共同拥有非标准的MRV结构。
展开▼
