Aggregate Loss Models to Calculate Risk Measures

Abstract

The concept of aggregate loss models pertains to a stochastic variable representing the total sum of all losses encountered within a set of insurance policies. In the non-life insurance sector, it is employed to assess the potential losses that an insurance company may face when claims made by policyholders exceed the allocated claim reserves. The purpose of studying aggregate loss models is to ascertain risk measures such as standard deviation of premium principles, value at risk (VaR), and conditional tail expectation (CTE). These steps aid insurance companies in the management and quantification of risks associated with aggregate losses. The standard deviation of premium principles is calculated analytically by substituting expected values and variances, while VaR is estimated using the Monte Carlo method to determine quantile values and confidence intervals. CTE is evaluated by computing the average losses that surpass the VaR threshold. These distributions and parameters require the Pareto distribution, which characterizes claim sizes, and the Poisson or Negative Binomial distribution, which factors in the number of claims. It is crucial to carefully consider the selection of the appropriate distribution, as it plays a significant role in determining the accuracy and reliability of the model. Furthermore, other influencing factors, such as loading factors and confidence intervals, should also be taken into account. These factors have the potential to significantly impact the quantification of risk arising from the model.