In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.

中文翻译：

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测试内部风险模型的偿付能力资本要求模型的变化

在 Solvency II 指令的背景下，内部风险模型的运行是风险评估和确定欧盟保险公司偿付能力资本要求的一种可能方式。Monte Carlo 程序通常用于生成模型输出。为了符合指令，内部风险模型的验证是在模型输出的基础上进行的。为此，我们建议进行一项新测试，以检查模型偿付能力资本要求是否发生重大变化。研究了检验统计量的渐近特性，并证明了自举逼近是合理的。模拟研究调查了有限样本情况下的测试性能，并证实了理论结果。内部风险模型和测试的应用在一个简化的例子中说明。该方法更普遍地用于基于配对样本推断一大类法律不变和连贯的风险度量。