Modeling Health Insurance Claims with Extreme Observations

In modeling insurance claims, when there are extreme observations in the data, the commonly used loss distributions are often able to fit the bulk of the data well but fail to do so at the tail.

One approach to overcome this problem is to focus only on the extreme observations and model them with the generalized Pareto distribution as supported by extreme value theory. However, this approach discards useful information about the small and medium-sized claims which is important for many actuarial purposes. In this study we consider modeling large skewed data using a highly flexible distribution, the generalized lambda distribution, and the recently proposed semiparametric transformed kernel density estimation.

Considering the medical claim of Iran insurance company in 1389 and 1390, we have observed that the data is strongly skewed to the right. By applying our models for no threshold data, the transformed kernel and GPD model fit well to medical claims but GLD model is not good enough in modeling higher claims. For claims above 15,000,000 all models fit the empirical data well. Finally, Value at Risk estimation is given. We suggest using the transformed kernel density to estimate loss distribution based on the results. Consequently, losses can be estimated more accurately. Also the relevant premium can be charged and as a result of that, insurance company can witness a decline in loss ratio.