Sufficient conditions for ordering aggregate heterogeneous random claim amounts

This note has a revisit to stochastic comparison on aggregate claim amounts. We develop sufficient conditions for the usual stochastic order on aggregate claim amounts of independent claim sizes and with a common occurrence frequency vector. Besides, we obtain the usual stochastic order on aggregate claim amounts with a common WSAI claim size vector, and this also improves Theorem 4.6 of Zhang and Zhao (2015).