Dynamic Mixtures of Copulas Using Wavelets with Actuarial Applications

Interconnected economic systems require effective ways to aggregate correlated risks. Currently, regulatory frameworks demand risk aggregation using linear dependencies through correlation matrices. This methodological simplicity is well known to regulators, who encourage insurers to improve their solvency capital allocation models by creating more robust internal models for measuring risk dependencies. One way to achieve this is by using dynamic mixtures of copulas – linear combinations of copulas weighted by time-varying factors used to assess the dynamics of the variation in the dependency structure. Although methods for determining these weights already exist, in this study we innovate by using wavelets to capture the dynamics of these factors, allowing a joint analysis in both time and frequency domains, indicating both the location and intensity of dependence, classified at different levels. This enabled the construction of a predictor for future risk dependence, which can be used as (i) a future solvency capital allocation indicator for the next periods, allowing insurers to allocate more/less capital and improving the management of their economic capital, and; (ii) a premium estimator for multi-risk policies. Application in automobile insurance showed that this prospective model generated (i) greater effectiveness in solvency capital allocation across various insurers assessed in the Brazilian market, performing better than the standard regulatory model, where the correlation matrix is altered retrospectively, and; (ii) more competitive premiums of comprehensive coverage compared to other insurers.