A New Robust Estimation and Hypothesis Testing for Reinsurance Premiums in Big Data Settings

This research study presents a novel methodology to estimate premiums for reassurance in the setting of large datasets, employing the principle of grouping. We present a median-of-means non-parametric estimator that addresses the difficulties posed by huge datasets. We analyze this estimator's consistency and asymptotic normality under specific criteria about the growth rate of subgroups. Furthermore, we introduce a novel approach to the empirical likelihood method for the median to evaluate excess-of-loss reinsurance. Our proposed method eliminates the need to estimate the estimator's variance structure in advance, which can be difficult and prone to inaccuracies. Numerical simulation analysis is implemented to evaluate the efficacy of our proposed estimator. The results indicate that our estimator is highly resilient in the presence of outliers.