Economic capital management for insurance companies

The loss ratio (LR) for insurance companies is defined as the ratio of incurred claims and earned premiums for a specified class of insurance (CoI). The company may estimate then its capital requirement for that particular CoI by using value at risk (VaR) or conditional VaR (CVaR) of the LR distribution at a specified probability value. The overall objective of the company is to evaluate the aggregate capital requirement through a weighted sum of marginal capital requirements for all the classes of insurance. Nevertheless, this procedure may tend to over-estimate the aggregate capital requirement because it does not take into consideration the real dependence among the different classes of insurance. In other words, perfect dependence does not allow considering diversification effects.