What Exactly Is Credibility Theory?
The term "credibility theory" refers to the tools, policies, and procedures that actuaries employ when analyzing data to estimate risk. Credibility theory employs mathematical models and methods to generate experience-based estimates, where "experience" refers to historical data.
Why Should You Use Credibility Theory?
The theory of credibility assists actuaries in understanding the risks associated with providing coverage and allows insurance companies to limit their exposure to claims and losses.
Insurance companies and actuaries create models based on historical losses, with the model incorporating a number of assumptions that must be statistically tested to determine their credibility. For example, an insurance company will look at previous losses from insuring a specific group of policyholders to estimate how much it will cost to insure a similar group in the future.
When creating an estimate, actuaries will start with a base estimate. A life insurance company, for example, may use a mortality table as the foundation of its base estimate because claims only arise when the insured dies.
Actuaries will use a variety of base estimates to cover the various aspects of the policy, including the prices charged by the insurance company for coverage.
How Credibility Theory Can Assist Actuaries
After establishing a base estimate, an actuary will examine the insurance company's historical experiences on a policy-by-policy basis. The actuary will examine this historical data to determine how the insurer's experience differed from that of other insurance companies.
The actuary will examine this historical data to determine how the insurer's experience differed from that of other insurance companies. The examination enables the actuary to generate various weights based on variances.
For example, it could categorize drivers based on their age, gender, and vehicle type, with a young man driving a fast car considered a high risk and an elderly woman driving a small car considered a low risk.
The division is made by balancing the two requirements that the risks in each group be sufficiently similar and the group be large enough for a meaningful statistical analysis of the claims experience to be performed in order to calculate the premium. As a result of this compromise, none of the groups contain only identical risks. The problem then becomes figuring out how to combine the group's experience with the individual risk's experience to arrive at a more appropriate premium. This problem is addressed by credibility theory.
In order to develop formulas, credibility theory ultimately relies on a combination of historical data experience estimates and base estimates. The formulas are used to recreate previous experiences before being tested against actual data.
When developing an initial estimate, actuaries may use a small data set, but large data sets are ultimately preferred because they have greater statistical significance.