Dependence Modeling in Non-Life Insurance: Copula Functions and Capital Adequacy - A Case Study of AXA Insurance.

The traditional modeling of dependence among branches in non-life insurance has historically rested on the assumption of independence between risks. However, recent studies have brought to light that overlooking the interdependence between risks is not prudent. An illustrative example is found in automobile insurance, where a discernible connection exists between the number of claims in the Automobile Damage branch and those in the Automobile Civil Liability branch. This paper aims to delve into the utilization of copula functions for modeling the interrelationships among claims charges across diverse branches within a non-life insurance portfolio. Moreover, it seeks to assess the consequential impacts of these dependencies on the capital requirements of AXA Insurance in the Moroccan market. Our research concentrates on four pivotal branches within AXA Insurance, namely "work accidents", "automobile civil liability", "disability", and "fire, marine, aviation, and transport". Through a thorough analysis encompassing dependency measurements, independence tests, and various graphical representations, we have substantiated the existence of interdependencies among the claim costs associated with these four risk branches. Importantly, our findings underscore that assuming independence leads to a slight underestimation of the capital requirement needed for effective risk accumulation management by the insurer. [ABSTRACT FROM AUTHOR]