Insurance Research CenterIranian Journal of Risk and Insurance1120150501Ordering Properties of the Smallest Claim Amount from Two Heterogeneous Generalized Exponential Portfolios and their Application to Insurance436343266ENGhobad BarmalzanPhD Candidate of Statistics, Shahid Beheshti UniversityAmir.T. Payandeh NajafabadiAssociate Professor, Shahid Beheshti UniversityJournal Article20150129<strong>Abstract</strong><br /> <em>Suppose </em> <em> is a set of non-negative random variables with </em> <em> having the distribution function generalized exponential, for </em> <em>, and </em> <em> are independent Bernoulli random variables, independent of the </em> <em>'s, with </em> <em>, </em> <em> . Let </em> <em> , for </em> <em> It is of interest to note that in actuarial science, it corresponds to the claim amount in a portfolio of risks.</em> <em>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 </em><em>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.</em>http://ijri.irc.ac.ir/article_43266_b1c5ac5b3809027904b638457170f156.pdf