Robust Loss Modeling for Claim Severity Data

Actuaries are required to predict the cost of uncertain future claims. Insurance claims are usually non-negative number, for example, automobile or liability insurance. The actuary's challenge is to determine an appropriate probability distribution that reflects the claims that will arrive in the next policy period. There are three challenges when constructing a probabilistic model. They are (1) past data are often affected by the presence of deductibles, policy limits and coinsurance, (2) past data may contain outliers (unusual observations that can distort the results), and (3) a need to evaluate the accuracy of the forecast. The contemporary literature in this area treats the three items as separate problems, leaving the practitioner with an incomplete framework for model building and assessment. This presentation will provide a comprehensive framework for addressing all three of these challenges simultaneously mainly via three estimation procedures: (a) maximum likelihood estimator (MLE), (b) dynamic method of trimmed moments (MTM), and (c) method of truncated moments (MTuM) including some other variants. Asymptotic distributional properties are established (along with extensive simulation studies) which are essential parts for statistical inferences. Numerical examples will be provided for 1500 US Indemnity Losses which illustrate the practical performance of the established results.