Pareto DistributionA heavy-tailed severity distribution with survival function S(x) = (theta/(theta+x))^alpha. Commonly used in insurance for large losses. Has finite mean only when alpha > 1 and finite variance only when alpha > 2.CensoringOccurs when the exact loss amount is not observed because it exceeds a policy limit. The observation is recorded as the limit value. The likelihood contribution for a censored observation is the survival function evaluated at the limit.TruncationOccurs when losses below a threshold (such as a deductible) are not observed at all. The likelihood must be conditioned on the loss exceeding the threshold, dividing each density by the survival function at the threshold.Buhlmann-Straub ModelAn extension of Buhlmann credibility that accommodates varying exposure levels across experience periods. The credibility weight is Z = sum(m_j) / (sum(m_j) + k), where m_j are the exposure weights.EVPV (Expected Value of the Process Variance)v = E[Var(X|theta)]. In Buhlmann credibility, it measures the average variability within each risk class. Combined with VHM, it determines the credibility factor k = v/a.VHM (Variance of the Hypothetical Means)a = Var(E[X|theta]). In Buhlmann credibility, it measures the variability between risk classes. A larger VHM means the classes are more distinct, leading to higher credibility for individual experience.Loss Development FactorThe ratio of cumulative losses at one maturity to cumulative losses at the previous maturity. Also called an age-to-age factor. Used in the chain-ladder method to project losses to their ultimate level.Cape Cod MethodA reserving method that estimates a single expected loss ratio from all accident years simultaneously, weighted by earned premium and expected development. A weighted average of chain-ladder and BF approaches.Value at Risk (VaR)VaR at confidence level alpha is the loss amount such that P(X > VaR) = 1 - alpha. It is the alpha-th quantile of the loss distribution. Widely used in risk management but not a coherent risk measure.Tail Value at Risk (TVaR)TVaR at level alpha is the expected loss given that the loss exceeds VaR_alpha: TVaR = E[X | X > VaR_alpha]. Also called Conditional Tail Expectation (CTE). It is a coherent risk measure.Coherent Risk MeasureA risk measure satisfying four axioms: translation invariance, subadditivity, positive homogeneity, and monotonicity. TVaR is coherent; VaR is not (it fails subadditivity for some distributions).RegularizationA technique to prevent overfitting by adding a penalty term to the loss function. LASSO (L1) shrinks some coefficients to exactly zero, performing variable selection. Ridge (L2) shrinks all coefficients toward zero without eliminating any.