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.