Severity DistributionThe probability distribution of the size of an individual loss. Common severity distributions in insurance include the Exponential, Pareto, Lognormal, Weibull, and Gamma.Frequency DistributionThe probability distribution of the number of losses in a given period. Common frequency distributions include the Poisson, Negative Binomial, and Binomial.Aggregate Loss DistributionThe 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 RecursionA 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.CredibilityA 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 CredibilityA 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 DevelopmentThe 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 MethodA 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 MethodA 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 PremiumHistorical 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 ValueE[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.