Vine copulas and fuzzy inference to evaluate the solvency capital requirement of multivariate dependent risks

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.