Description: This is a concluding and encompassing part of our research on the project entitled \Weighted Premium Calculation Principles and Risk Capital Allocations, which has been supported by the Actuarial Education and Research Fund AERF and the Society of Actuaries Committee on Knowledge Extension Research CKER. We explore the concept of weighted distributions and their role in various phenomena occurring in insurance and finance. In particular, we relate weighted distributions to actuarial and economic premium calculation principles, and also to the capital asset pricing model CAPM. Imitating the latter, we propose a weighted insurance pricing model WIPM. Although general in formulation, we show that the WIPM can successfully be evaluated in a variety of situations, which we illustrate with a number of examples.

Description: The concept of transformed distributions is generalized in this paper. First the concepts of net premium intensity, loaded premium intensity and load generators arc introduced. Then transformed distributions are identified with premium intensity and hence the loaded premium is calculated from transformed distributions. Finally it is shown that this method of premimn calculation is arbitrage free and it incorporates the strengths of the utility approach.