Credibility Theory

Key Takeaways

• Actuaries use credibility theory to estimate insurer risks.
• Bayesian and Bühlmann models are key methods used in credibility theory.
• Insurance companies use credibility theory to adjust premiums and loss reserves.
• The theory combines historical data with base estimates for accurate predictions.
• Actuaries prefer large data sets for greater statistical significance in estimates.

What Is Credibility Theory?

Credibility theory refers to how actuaries assess data to estimate the risk insurers face when providing coverage to policyholders. It helps insurance companies to limit their exposure to financial losses. Credibility theory uses mathematical models to provide relevant estimates based on historical data. Much of creditability theory rests on Bayesian statistics. The Buhlmann, or Cape Cod, model is used by insurers to estimate a credible interval for their loss reserves.

How Credibility Theory Works in Practice

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 their credibility.

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 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.

The Role of Credibility Theory in Actuarial Analysis

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.

Tip

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.

Exploring Different Types of Credibility Theory

Bayesian Theory

Bayesian statistics is a method of understanding the probabilities of outcomes based on knowledge of previous outcomes. Bayes' theorem allows one to update or revise understandings of the world as new information about prior events comes in.

In standard statistical methods, outcomes or expectations are often described by their confidence interval, or the probability that an outcome will appear as expected (often set with a level of 95% confidence). Because Bayesian statistics instead relies on prior and posterior estimations of possible outcomes, it instead uses a "credible interval" (also usually set at 95% credibility).

Buhlmann Theory

Similar to Bayes' theorem, Bühlmann creditability relies on past experience to update estimates and provide a credible interval. The Bühlmann model (sometimes called the Cape Cod model) applies random effects to prior experience to come up with proportional weighting. This model is used by actuaries and insurance companies to calculate their loss reserves.

Who Developed the Credibility Theory?

Credibility theory is often attributed to the work of Thomas Bayes in the 18th century. The goal of credibility is to make more accurate forecasts of future events (which are uncertain) by incorporating new information as it arises to update and revise those forecasts.

What Is Credibility in Actuarial Science?

Actuaries and insurers use credibility theory to help estimate the number of claims they will expect to pay out in a given year, and whether the premiums they receive from policyholders will be sufficient to cover those outflows. The theory allows them to update their estimates as new loss and claims experience is received.

What Is Source Credibility Theory?

In behavioral economics, source credibility theory states that people are more likely to be persuaded by a source if he or she is considered to be credible. It is the perceived level of trust or expertise held by a person, and not what they actually say, that matters.