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Abstract:
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In actuarial practice, maximum likelihood estimation (MLE) is an exclusively adopted approach to estimate parameters of claim distributions. Despite its popularity, MLE often suffers from robustness issues where small model contaminations can heavily distort the estimated model, providing misleading insurance pricing and risk management information. To alleviate the above robustness problem, we propose a maximum weighted likelihood estimator (MWLE), which reduces the weights of the observations likely to lead to a lack of robustness. Asymptotic theories are developed to ensure that MWLE is consistent and asymptotically normal so that model uncertainties can be easily quantified. The proposed MWLE is also highly versatile, as it can be easily extended to cater to several mechanisms prevalent in insurance practice, including the impacts of policyholder attributes (regression) and loss control mechanisms (data censoring and truncation). Furthermore, we create a Wald-based test statistic based on the MWLE, a diagnostic tool to quantitatively detect systematic incoherence of fitted model classes, providing recommendations on whether it is worthwhile to explore alternative model classes.
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