When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (i) models should be designed to accommodate deductibles, policy limits, and coinsurance factors, (ii) parameters should be estimated robustly to control the...

A single-parameter Pareto model, Pareto I, arises in many areas of application such as pricing of insurance risks, measuring income or wealth inequality in economics, or modeling lengths of telephone calls in telecommunications. In insurance, for example, it is common to work with data that are...

Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity...

With some regularity conditions maximum likelihood estimators (MLEs) al-ways produce asymptotically optimal (in the sense of consistency, efficiency, sufficiency,and unbiasedness) estimators. But in general, the MLEs lead to non-robust statisticalinference, for example, pricing models and risk...

Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as...

Many quantities arising in non-life insurance depend on claim severity distributions, which are usually modeled assuming a parametric form. Obtaining good estimates of the quantities, therefore, reduces to having good estimates of the model parameters. However, the notion of ‘good estimate'...

In actuarial practice, regression models serve as a popular statistical tool for analyzing insurance data and tariff ratemaking. In this paper, we consider classical credibility models that can be embedded within the framework of mixed linear models. For inference about fixed effects and...