Usual Stochastic Order of Aggregate‎ Claim Amounts from Two Marshall-Olkin Extended‎ Weibull Portfolios

‎‎In this paper‎, ‎we discuss the stochastic comparison of two‎ classical surplus processes in an one-year insurance period‎. ‎Under‎ the Marshall-Olkin extended Weibull random aggregate claim‎ amounts‎, ‎we establish some sufficient conditions for the‎ comparison of aggregate claim amounts in the sense of the usual‎ stochastic order (which implies stop-loss order)‎. ‎Applications of our results to the Value-at-Risk and‎ ruin probability are also given‎. ‎The obtained results show that the heterogeneity of the risks in a given‎ insurance portfolio tends to make the portfolio volatile‎, ‎which in turn leads to requiring more‎ capital‎.