ABDULAI ABUBAKAR-SADIQ

APPLIED MULTIVARIATE STATISTICAL ANALYSIS

PROJECT PROPORSAL: APPLICATION OF PRINCIPAL COMPONENTS ANALYSIS TO INSURANCE GROSS WRITTEN PREMIUMS

Insurance of any type is all about managing risk. The insurance industry is basically divided into life and nonlife (or property and casualty insurance). An insurance company collects premiums from policy holders, invests the money and then reimburses this money when the insured perils occur.

Property and casualty insurance protects against loss to one’s business, home or other property which may result from injury or damage to the property of others.

The insurance industry plays a major role in the economy of every country. World insurance premiums increased from $4.11 trillion in 2009 to $4.34 trillion in 2010. And analysts say the financial performance and condition of insurers continues to show recovery and improvement from the decline during the 2008 financial crisis.

This project aims at offering a statistical analysis of the world insurance market for the year 2012 by analyzing gross written premiums. We use principal components analysis (PCA) to examine whether there are common factors that explain relationships among the kinds of insurance policies offered in world’s the property and casualty industry.

Specifically, this project will apply the principal component analysis as an exploratory method to studying the following property and casualty insurance classes by gross written premiums:

1. Motor vehicle insurance2. Marine and other transport insurance3. Freight insurance4. Fire and other property damage insurance5. Pecuniary loss insurance6. General liability insurance7. Accident and health insurance8. Other nonlife insurance

It is our hope that we can extract relevant indicators, on which we can achieve an understanding of the interplay between the said classes. With data from Organization for Economic Cooperation and Development (OECD), we analyze gross written premiums from the world’s largest insurance markets, which consists of 9 non-OECD countries and 34 member countries of OECD that span the globe, from

North and South America to Europe and the Asia-Pacific region. They include not only the world’s most advanced countries but also emerging countries like Mexico, Chile, Columbia and Turkey.

Principal components analysis is a multivariate statistical technique that aims at extracting a small number of latent factors responsible for the correlations between the original variables to recover as much of the total information contained in the original data. If these correlations are significant, we can assume that would be caused by the existence of one or more hidden factors common to all variables.

For data reduction, the principal components method of extraction begins by finding a linear combination of variables (a component) that accounts for as much variation in the original variables as possible. It then finds another component that accounts for as much of the remaining variation as possible and is uncorrelated with the previous component, it continues in this manner until there are as many components that account for a significant portion of the information inherent in the original variables. Usually, a few components will account for most of the variation, and these components will reasonably represent the original variables.