Ordering Properties of the Smallest Claim Amount from Two Heterogeneous Generalized Exponential Portfolios and their Application to Insurance


1 PhD Candidate of Statistics, Shahid Beheshti University

2 Associate Professor, Shahid Beheshti University


Suppose   is a set of non-negative random variables with  having the distribution function generalized exponential, for , and   are independent Bernoulli random variables, independent of the 's, with ,  . Let  , for  It is of interest to note that in actuarial science, it corresponds to the claim amount in a portfolio of risks. In this paper, it’s been tried to discuss the stochastic comparison between the smallest claim amounts in the sense of the usual stochastic order using the concept of vector weakly submajorization and under certain conditions. We obtain the usual stochastic order between the smallest claim amounts when the matrix of parameters  changes to another matrix in a mathematical sense and finds an upper bound for the survival function of smallest claim amount. The results established here extend some well-known results in the literature and show that larger stochastic order smallest claim amount lead to the desirable property of uniformly larger Value-at-Risk.