individual risk model
Imagine a one-year group life scheme covering 1,000 named employees. You want the distribution of next year's total payout. The most direct way is to walk through the list person by person: each one either makes a claim (with their own probability and benefit) or does not, and you add up everyone's outcome. That person-by-person, add-them-all approach is the individual risk model.
Formally, the aggregate loss S is a sum of a fixed number of independent terms, one per policy: S = X1 + X2 + ... + Xn, where n is the known number of policies and each Xi is the loss from policy i (often zero, since most policies do not claim). Crucially the number of terms n is fixed in advance and the policies can differ — different ages, sums insured, claim probabilities. The expected total is the sum of the individual expected losses, and (under independence) the variance is the sum of the individual variances. For groups of similar size the central limit theorem often makes S roughly normal, which is handy for setting premiums and reserves.
The individual risk model is the natural framework for short-term group insurance — group life and group health, where membership is a known list for the period. Its defining feature, and limitation, is that n is fixed: it models 'each of these specific n policies' rather than 'a random number of claims from a portfolio'. That contrasts with the collective risk model, which lets the claim count itself be random. For a homogeneous, large portfolio the collective model is often more convenient and the two broadly agree; for a heterogeneous, enumerable group the individual model is the honest representation. The usual assumption of independence between policies can fail badly under a common shock (a pandemic, a building collapse) that hits many lives at once.
A group covers 3 employees. Employee A: claim probability 0.01, benefit 100,000. B: 0.02, 50,000. C: 0.005, 200,000. Expected total = 0.01 times 100,000 + 0.02 times 50,000 + 0.005 times 200,000 = 1,000 + 1,000 + 1,000 = 3,000. The full distribution of S is found by considering every combination of who claims, summing the benefits in each case.
Sum a fixed list of independent policies — each may or may not claim its own benefit.
The independence assumption breaks under a common shock that hits many policies at once (an epidemic, a single fire in a group of co-located lives). When losses are correlated, summing individual variances understates the true variability of the total.