ABSTRACT

A capital requirement should be established for insurance companies at a level that allows them to fulfil their engagements towards policyholders. As such, evaluating an accurate amount of reserve and capital within different lines of business is a fundamental procedure for any company. However, studying the dependence between lines of business and the uncertainty regarding this dependence has been neglected in prior actuarial research. In practice, the evaluation of a Solvency Capital Requirement may be inaccurate when the risks of different business lines are independent. Thus, the present article aims to provide an appropriate modelling approach for claim amounts by taking into account the multivariate dependence between risks. To alleviate this issue, it uses vine copula functions to capture dependence between multivariate distributions of risks for five lines of business. Moreover, the dependence structure may be uncertain which leads to determining different levels of capital. Therefore, we propose a fuzzy inference system to handle the uncertainty of dependence structure. The obtained results reveal that considering the multivariate dependence structure produces a higher amount of Solvency Capital Requirement than the independence case. Moreover, the Solvency Capital Requirement level is decided according to the degree of dependence between risks.

摘要

应为保险公司制定资本要求，使其能够履行对保单持有人的承诺。因此，评估不同业务范围内准确数量的储备和资本是任何公司的基本程序。然而，在先前的精算研究中，研究业务线之间的依赖性以及这种依赖性的不确定性一直被忽视。在实践中，当不同业务条线的风险相互独立时，偿付能力资本要求的评估可能不准确。因此，本文旨在通过考虑风险之间的多变量相关性，为索赔金额提供适当的建模方法。为了缓解这个问题，它使用 vine copula 函数来捕捉五个业务线的多元风险分布之间的依赖关系。此外，依赖结构可能是不确定的，这导致确定不同的资本水平。因此，我们提出了一个模糊推理系统来处理依赖结构的不确定性。获得的结果表明，考虑多元依赖结构会产生比独立情况更高的偿付能力资本要求。此外，偿付能力资本要求水平是根据风险之间的依赖程度决定的。获得的结果表明，考虑多元依赖结构会产生比独立情况更高的偿付能力资本要求。此外，偿付能力资本要求水平是根据风险之间的依赖程度决定的。获得的结果表明，考虑多元依赖结构会产生比独立情况更高的偿付能力资本要求。此外，偿付能力资本要求水平是根据风险之间的依赖程度决定的。