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

29 Pages Posted: 22 Dec 2016 Last revised: 23 Jun 2018

See all articles by Wenjun Zhu

Wenjun Zhu

Nanyang Business School, Nanyang Technological University

Ken Seng Tan

University of Waterloo

Lysa Porth

University of Manitoba - Warren Centre for Actuarial Studies and Research; University of Waterloo - Department of Statistics and Actuarial Science; University of Manitoba - Department of Agribusiness and Agricultural Economics

Date Written: December 21, 2016

Abstract

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.

Keywords: Premium Principle, Weighted Distribution, Weighted Transform, Stochastic Dominance, Insurance Pricing, Economic Premium

Suggested Citation

Zhu, Wenjun and Tan, Ken Seng and Porth, Lysa, On a Class of Premium Calculation Principles Based on the Multivariate Weighted Distribution (December 21, 2016). Available at SSRN: https://ssrn.com/abstract=2888702 or http://dx.doi.org/10.2139/ssrn.2888702

Wenjun Zhu (Contact Author)

Nanyang Business School, Nanyang Technological University ( email )

50 Nanyang Avenue
Singapore, 639798
Singapore
(65) 6592-1859 (Phone)

HOME PAGE: http://sites.google.com/view/wenjun-zhu

Ken Seng Tan

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Lysa Porth

University of Manitoba - Warren Centre for Actuarial Studies and Research ( email )

638 Drake Centre, 181 Freedman Crescent
Winnipeg, MB R3T 2N2
Canada

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

University of Manitoba - Department of Agribusiness and Agricultural Economics ( email )

Winnipeg, MB, R3T 2N2
Canada

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