On a Class of Premium Calculation Principles Based on the Multivariate Weighted Distribution

This paper proposes a new class of premium calculation principles based on the multivariate weighted distribution, where risk loadings are imposed by transforming the density of the underlying actuarial risk by encompassing a number of external risk factors. This is a highly flexible class of premium principle with a number of desirable characteristics, including scale and translation invariance, additivity, stochastic dominance preserving, and additivity for layers. It is also shown that by appropriately selecting external risk factors, this premium principle has increasing relative risk loading. This is important for pricing layered insurance contracts, which is common for many property and casualty insurance programs, such as for agriculture, hurricanes, etc. This premium principle is important for actuarial pricing practice in the sense that it is able to integrate additional important information into the pricing framework, such as market conditions, economic conditions, catastrophic events, etc. Two pricing examples are presented to demonstrate the statistical advantages and empirical application of the new premium principle proposed in this paper