# Credibility Theory

## What Is Credibility Theory?

Credibility theory refers to tools, policies and procedures used by actuaries when examining data in order to estimate risk. Credibility theory uses mathematical models and methods for making experience-based estimates, in which “experience” refers to historical data.

## Why Use Credibility Theory?

Credibility theory helps actuaries understand the risks associated with providing coverage, and it allows insurance companies to limit its exposure to claims and losses. Insurance companies and actuaries develop models based on historical losses, with the model taking into account a number of assumptions that have to be statistically tested in order to determine how credible they are. For example, an insurance company will examine losses previously incurred from insuring a particular group of policyholders in order to estimate how much it may cost to insure a similar group in the future.

When developing an estimate, actuaries will first select a base estimate. For example, a life insurance company may select a mortality table as the backbone of its base estimate, since claims only arise when the insured dies. Actuaries will use a variety of base estimates to cover the different aspects of type of policy, including the prices that the insurance company typically charges for coverage.

## How Credibility Theory Helps Actuaries

Once a base estimate is established, an actuary will then look through the insurance company’s historical experiences on a policy-by-policy basis. The actuary will study this historical data to see how the insurer’s experience may have differed from the experience of other insurance companies. The examination allows the actuary to create different weights based on variances.

For example, it might divide motorists by age, sex, and type of car; a young man driving a fast car being considered a high risk, and an old woman driving a small car being considered a low risk. The division is made balancing the two requirements that the risks in each group are sufficiently similar and the group sufficiently large that a meaningful statistical analysis of the claims experience can be done to calculate the premium. This compromise means that none of the groups contains only identical risks. The problem is then to devise a way of combining the experience of the group with the experience of the individual risk to arrive at a more appropriate premium. Credibility theory provides a solution to this problem.

Credibility theory ultimately relies on the combination of experience estimates from historical data as well as base estimates in order to develop formulas. The formulas are used to replicate past experiences, and are then tested against actual data. Actuaries may use a small data set when creating an initial estimate, but large data sets are ultimately preferred because they have greater statistical significance.

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