Ordering Results for Aggregate Claim Amounts from Two Heterogeneous Marshall--Olkin Extended Exponential Portfolios and Their Applications in Insurance Analysis

In this work, we discuss the stochastic comparison of two classical surplus processes in a one-year insurance period. Under the Marshall--Olkin extended exponential random aggregate claim amounts, we extend one result of Khaledi and Ahmadi [J. Statist. Plann. Inference, 138 (2008), pp. 2243--2251]. Applications of our results to the value-at-risk and ruin probability are also given. Our 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.