Orderings of Extreme Claim Amounts from Heterogeneous and Dependent Weibull-G Insurance Portfolios

Abstract

In the context of insurance, the smallest and largest claim amounts become increasingly important in the context of insurance analysis, which provides crucial and key information for setting an annual premium. We first give some sufficient conditions for comparing the largest claim amounts arising from two sets of dependent heterogeneous Weibull-G insurance portfolios with respect to the usual stochastic order under Archimedean copula dependence. Second, we establish some sufficient conditions to compare the smallest claim amounts in the sense of the usual stochastic and hazard rate orders when the claim severities are independent or dependent heterogeneous Weibull-G insurance portfolios. Finally, to illustrate the key theoretical insights, some numerical examples are offered.