The paper was divided into three parts. In the ?rst chapter, we intro-duced some elementary knowledge about premium calculation principle.In the second chapter, we ?rst gave properties on the Zero utility pre-mium principle and the mean value premium principle. Then we obtainedthe su?cient-necessary condition about their proportionality respectively.Moreover we establish a k-order mean value principle and derive its someproperties. In the last chapter, we study insurance companies how tocooperate with each other in decreasing premium and increasing marketcompetency . Particularly, we acquired the minimal premium and eachcompany should insure a certain percentage of the given risk when all ofthem used variance premium calculation principle.
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