Ordering results between the largest claims arising from two general heterogeneous portfolios

TL;DR

This paper compares the largest claims from two diverse insurance portfolios using stochastic orderings, providing conditions based on model parameters and illustrating applications for better risk assessment.

Contribution

It introduces new sufficient conditions for comparing largest claims in heterogeneous portfolios using stochastic orderings, based on matrices and vectors of model parameters.

Findings

Established conditions for stochastic ordering of largest claims

Applicable to a broad family of distribution models

Illustrated with practical examples

Abstract

This work is entirely devoted to compare the largest claims from two heterogeneous portfolios. It is assumed that the claim amounts in an insurance portfolio are nonnegative absolutely continuous random variables and belong to a general family of distributions. The largest claims have been compared based on various stochastic orderings. The established sufficient conditions are associated with the matrices and vectors of model parameters. Applications of the results are provided for the purpose of illustration.