How is statistics used in insurance?

Although statistics is important in many types of business, it is particularly important to the insurance industry. Statistics is used to determine what risk an insured poses to an insurance company, what percentage of policies is likely to pay out, and how much money a company can expect to pay out in claims.

An actuary is a person trained in investment strategies and statistical tools. Actuaries need to know investment strategies in insurance because of the diverse range of products in the insurance field. For example, an actuary may be working with pensions and retirements under a life insurance umbrella. Actuaries are required to pass tough examinations in almost every country to demonstrate they have a sound knowledge of probability and statistics.

Statistics isn't an exact science: actuaries look at statistical data and make a best guess at what the data is telling them. In order to prepare for making decisions, actuaries study decision theory, a subset of mathematics and statistics that includes game theory. Game theory helps an actuary to understand what a person is likely to do and why. For example, if an auto insurance policy holder goes into debt, he may be more likely to file a false claim on his vehicle to make money. There are no definite figures for this type of human behavior; the decision to charge a higher premium for certain risks is made by the actuary based on his knowledge base.

A loss distribution can give an actuary a picture of claim behavior over a certain period or show how categories of claims stack up against each other. For example, an actuary might construct a histogram, a type of bar graph that compares categories. The bar graph might show how claims relate to age groups for life insurance. The actuary will be able to look at trends and see if higher premiums for certain age groups are warranted.

A linear model can be used to see if one category or item is related to another. An example of a linear model is linear regression: data points are plotted on a graph to see if they have a linear relationship; in other words, can a straight line be used to represent the data. If a straight line can be drawn, this indicates that there is a relationship between the two categories. A linear model can be used to find out information about how age, gender, salary and other characteristics relate to claim size.

A time series model is where an actuary looks at how a particular item performs over time. For example, they may look at how policyholders' claims history changes over time to determine how much to charge for specific policyholder characteristics or they may study the performance of investments over a period of time to determine rates to charge for whole life insurance policies.