Some new conditions for the increasing convex comparison of risks

Abstract

The preservation under convolutions and mixing of the increasing convex comparison of risks is considered, and new related results are proved. Some applications of these results in actuarial context are shown. Also, similar properties are shown to be satisfied by the convex and the Laplace comparisons of risks.

Key words:

• Stochastic orders
• increasing convex order
• convex order
• Laplace order
• collective risk model
• random summations of risks
• random evaluations of collective risk models