MAS-II key terms

A set of statistical methods for updating a group rate with an individual insured's own experience, weighting each by how much data each contains. The result blends collective and individual information into a single estimate.

The weight, usually between zero and one, assigned to the insured's own observed experience when blending it with the manual or collective rate. Larger values mean the individual data are trusted more.

A credibility model in which the credibility factor equals exposure divided by exposure plus the ratio of expected process variance to variance of hypothetical means. It assumes linear estimation and is the foundation for many later models.

An extension of Bühlmann credibility that allows each observation to carry a different weight, such as varying exposure or policy counts. The credibility factor then reflects the total weight relative to the variance components.

The class of credibility procedures derived by minimizing expected squared error of the estimate, rather than relying on a fixed formula. Bühlmann and Bayesian credibility are examples of estimators built on this principle.

A credibility approach in which the prior distribution of the unknown risk parameter is specified and the posterior mean given the data is used as the estimate. It is exact under the assumed model but requires full distributional assumptions.

The average, over the prior distribution of risk parameters, of the variance of outcomes within a single risk class. It measures the random noise in individual observations and appears in the denominator of the Bühlmann credibility factor.

The variance across risk classes of the conditional expected outcome for each class. It measures how much true heterogeneity exists among risks and drives how much weight individual experience deserves.

A prior distribution whose posterior distribution belongs to the same family after observing data. It makes Bayesian updating tractable, for example a gamma prior with a Poisson likelihood yielding a gamma posterior.

The updated probability distribution of an unknown parameter after combining the prior distribution with observed data through Bayes' theorem. Its mean or another summary is used as the credibility estimate.

The expected claim cost per unit of exposure, typically pure premium, before loading for expenses and profit. It is the quantity credibility procedures usually estimate and blend.

A published or collective rate based on broad class experience rather than an individual insured's own results. It serves as the complement or prior value in credibility weighting.

A credibility standard based on the probability that observed experience falls within a specified percentage of the true expected value. It sets the minimum exposure needed for full credibility without modeling heterogeneity.

The exposure or claim count at which an insured's own experience is assigned a credibility weight of one, so the manual rate is ignored. It is often expressed as a standard based on claim frequency.

The situation where observed experience is credible enough to influence but not replace the manual rate, so the two are blended with weights between zero and one. The weight usually grows with the square root of exposure.

A ratemaking procedure that adjusts an insured's prospective premium using its own past loss experience relative to expected losses. Credibility weighting determines how much of the observed difference is carried forward.

A multiplicative factor applied to manual premium that reflects an insured's past losses compared with expected losses for its class. Values above one indicate worse-than-expected experience and increase the premium.

A multiplicative factor applied to losses at one evaluation age to estimate their ultimate value at a later maturity. It reflects the expected pattern of reported and paid claim growth over time.

A reserving technique that estimates ultimate losses by applying age-to-age development factors derived from historical triangles to the latest diagonal of cumulative losses. It assumes development patterns are stable across accident years.

A reserving method that combines an a priori expected loss estimate with reported losses, weighting them by the proportion of expected development still to emerge. It is more stable than chain ladder for immature accident years.

A reserving approach that estimates ultimate losses as a selected expected loss ratio multiplied by earned premium, ignoring reported losses. It is used when data are too immature for development methods.

The reserve for claims that have occurred but have not yet been reported to the insurer as of the valuation date. It is estimated from development patterns and expected loss ratios.

The reserve for changes in the estimated value of claims already reported, reflecting additional development on known claims. It is separate from the reserve for claims not yet reported.

The amount set aside by a claims adjuster for a specific reported claim based on the expected ultimate cost of that claim. Summing case reserves gives the reported loss liability before additional development.

The total estimated cost of all claims arising from a given accident period once all development is complete. Reserving methods project reported losses to this final value.

Incurred losses divided by earned premium for a period. It measures the share of premium consumed by claims and is a common input to expected loss ratio reserving.

A regression framework that relates a response variable to predictors through a link function and assumes a distribution from the exponential family. It underlies many modern insurance pricing models.

The function that connects the expected value of the response variable to the linear predictor in a generalized linear model. For example, the log link makes multiplicative effects additive on the log scale.

A family of distributions with a point mass at zero and a continuous positive part, controlled by a power parameter. It is widely used to model aggregate claim cost when zeros and positive amounts occur together.

A pricing approach that models claim frequency and average claim severity separately, then multiplies their predictions to obtain expected loss cost. Each component can use its own distribution and predictors.

A generalized linear model for count data that assumes the response has a Poisson distribution with mean linked to predictors, often by a log link. It is commonly used to model claim counts.

The situation where observed variance exceeds the variance assumed by the model, such as counts more variable than Poisson. It causes underestimated standard errors and suggests a different distribution or random effects.

A count regression model that allows the variance to exceed the mean by including an extra dispersion parameter. It is often preferred to Poisson regression when claim counts are overdispersed.

A generalized linear model in which the logarithm of the expected response is a linear combination of predictors. Coefficients act multiplicatively on the response, a natural fit for insurance relativities.

A measure of model fit equal to twice the difference between the log-likelihood of the saturated model and that of the fitted model. Smaller deviance indicates a better fit for a given distribution.

A model selection statistic equal to deviance plus twice the number of parameters, penalizing complexity. Lower values indicate a better trade-off between fit and parsimony.

An extension of a generalized linear model that includes random effects to capture correlation or unobserved heterogeneity among groups. It is used when observations within a cluster are not independent.

The final premium estimate formed by weighting the insured's own experience with the collective or manual premium according to credibility. It is the practical output of credibility theory.