Ordering Results of Aggregate Claim Amounts from Two Heterogeneous 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. 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. We also obtain some sufficient conditions for comparing aggregate non-random claim amounts with different occurrence frequency vectors in terms of increasing convex order.