Credibility Theory
Encyclopedia
Credibility theory is a branch of actuarial science
. It was developed originally as a method to calculate the risk premium
by combining the individual risk experience with the class risk experience.
When an insurance
company calculates the premium it will charge, it divides the policy holders into groups. 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 the better to calculate the premium. Credibility theory provides a solution to this problem.
For actuaries
, it is important to know credibility theory in order to calculate a premium for a group of insurance contract
s. The goal is to set up an experience rating system to determine next year's premium, taking into account not only the individual experience with the group, but also the collective experience.
There are two extreme positions: One is to charge the same premium to everyone, estimated by the overall mean
of the data. This makes sense only if the portfolio is homogeneous, which means that all risks cells have identical mean claims. However, if the portfolio is not homogeneous, it is not a good idea to charge premium in this way, since the "good" risks will take their business elsewhere (overcharging "good" people and undercharging "bad" risk people), leaving the insurer with only bad risks. This is an example of adverse selection
.
The other way around is to charge to group
its own average claims, being 
as premium charged to the insured. These methods are used if the portfolio is heterogeneous, provided a fairly large claim experience. To compromise these two extreme positions, we take the weighted average
of these two extremes:
has the following intuitive meaning: it expresses how "credible" (acceptability) the individual of cell 
is. If it is high, then use higher 
to attach a larger weight to charging the 
, and in this case, 
is called a credibility factor, such a premium charged is called a credibility premium.
If the group were completely homogeneous then it would be reasonable to set
, while if the group were completely heterogeneous then it would be reasonable to set 
. Using intermediate values is reasonable to the extent that both individual and group history are useful in inferring future individual behavior.
Actuarial science
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. Actuaries are professionals who are qualified in this field through education and experience...
. It was developed originally as a method to calculate the risk premium
Risk premium
A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset, in order to induce an individual to hold the risky asset rather than the risk-free asset...
by combining the individual risk experience with the class risk experience.
When an insurance
Insurance
In law and economics, insurance is a form of risk management primarily used to hedge against the risk of a contingent, uncertain loss. Insurance is defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for payment. An insurer is a company selling the...
company calculates the premium it will charge, it divides the policy holders into groups. 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
Statistical significance
In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. The phrase test of significance was coined by Ronald Fisher....
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 the better to calculate the premium. Credibility theory provides a solution to this problem.
For actuaries
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
, it is important to know credibility theory in order to calculate a premium for a group of insurance contract
Insurance contract
In insurance, the insurance policy is a contract between the insurer and the insured, known as the policyholder, which determines the claims which the insurer is legally required to pay. In exchange for payment, known as the premium, the insurer pays for damages to the insured which are caused by...
s. The goal is to set up an experience rating system to determine next year's premium, taking into account not only the individual experience with the group, but also the collective experience.
There are two extreme positions: One is to charge the same premium to everyone, estimated by the overall mean
of the data. This makes sense only if the portfolio is homogeneous, which means that all risks cells have identical mean claims. However, if the portfolio is not homogeneous, it is not a good idea to charge premium in this way, since the "good" risks will take their business elsewhere (overcharging "good" people and undercharging "bad" risk people), leaving the insurer with only bad risks. This is an example of adverse selectionAdverse selection
Adverse selection, anti-selection, or negative selection is a term used in economics, insurance, statistics, and risk management. It refers to a market process in which "bad" results occur when buyers and sellers have asymmetric information : the "bad" products or services are more likely to be...
.
The other way around is to charge to group
its own average claims, being as premium charged to the insured. These methods are used if the portfolio is heterogeneous, provided a fairly large claim experience. To compromise these two extreme positions, we take the weighted averageWeighted mean
The weighted mean is similar to an arithmetic mean , where instead of each of the data points contributing equally to the final average, some data points contribute more than others...
of these two extremes:
has the following intuitive meaning: it expresses how "credible" (acceptability) the individual of cell is. If it is high, then use higher to attach a larger weight to charging the , and in this case, is called a credibility factor, such a premium charged is called a credibility premium.If the group were completely homogeneous then it would be reasonable to set
, while if the group were completely heterogeneous then it would be reasonable to set . Using intermediate values is reasonable to the extent that both individual and group history are useful in inferring future individual behavior.