Individual vs. Collective Risk Models
Compare individual and collective risk models for aggregate loss distributions on Exam STAM.
Individual Risk Model
The individual risk model considers a fixed portfolio of n independent policies. Each policy i has its own claim probability q_i and severity distribution. Aggregate losses S = sum of X_i across all policies, where X_i is the loss from policy i (zero if no claim). The mean and variance of S are sums of individual means and variances. This model is realistic but computationally intensive for large portfolios, since each policy may have different parameters.
Collective Risk Model
The collective risk model treats aggregate losses as S = X_1 + X_2 + ... + X_N, where N is a random claim count and X_i are i.i.d. claim amounts independent of N. This simplification enables powerful computational tools like moment generating functions, Panjer recursion, and simulation. The mean of S equals E[N] times E[X], and the variance equals E[N] times Var(X) plus Var(N) times (E[X])^2. Exam STAM heavily favors the collective model for computing aggregate loss probabilities and stop-loss premiums.