STAM Glossary

Key terms and definitions for Exam STAM: Short-Term Actuarial Mathematics. Use this reference to review the most important concepts tested on the exam.

Severity Distribution
The probability distribution of the size of an individual loss. Common severity distributions in insurance include the Exponential, Pareto, Lognormal, Weibull, and Gamma.
Frequency Distribution
The probability distribution of the number of losses in a given period. Common frequency distributions include the Poisson, Negative Binomial, and Binomial.
Aggregate Loss Distribution
The distribution of total losses S = X_1 + X_2 + ... + X_N, where N is the random number of claims and X_i are individual claim amounts. Often modeled as a compound distribution.
Panjer Recursion
A recursive formula for computing the aggregate loss distribution when the frequency belongs to the (a,b,0) class. Allows exact computation of P(S = x) for discretized severity distributions.
Credibility
A technique for combining individual experience with group experience to produce an estimate. The credibility-weighted estimate is Z * (individual mean) + (1-Z) * (group mean), where Z is the credibility weight.
Buhlmann Credibility
A credibility model where Z = n / (n + k), with k = v/a. Here v = E[Var(X|theta)] is the expected process variance and a = Var(E[X|theta]) is the variance of the hypothetical means.
Loss Development
The process by which reported or paid losses change over time as claims are reported, adjusted, and settled. Development factors quantify how losses at one maturity relate to losses at a later maturity.
Chain-Ladder Method
A reserving technique that uses historical development patterns (age-to-age factors) to project reported or paid losses to their ultimate values. Assumes that past development patterns will continue.
Bornhuetter-Ferguson Method
A reserving method that blends the chain-ladder projection with an a priori expected loss estimate. Less sensitive to early development volatility than pure chain-ladder, making it preferred for immature accident years.
IBNR (Incurred But Not Reported)
Reserves set aside for claims that have occurred before the valuation date but have not yet been reported to the insurer. Estimating IBNR is a core actuarial function in reserving.
On-Level Premium
Historical premium adjusted to reflect the current rate level. Required in ratemaking to ensure that experience period premiums are comparable to the rates that will apply during the future policy period.
Limited Expected Value
E[X ^ d] = E[min(X, d)] = integral from 0 to d of S(x) dx. Represents the expected payment by the policyholder up to the deductible, or equivalently, the expected retained loss.