Reinsurance mathematics begins with the collective risk model. Aggregate losses \\(S\\) over a period are the sum of a random number \\(N\\) of individual claim amounts \\(X_i\\):
Under the standard assumptions, the mean and variance of aggregate loss follow from the frequency and severity moments:
Frequency and severity
Frequency \\(N\\) is often modeled with the Poisson or negative binomial distribution; severity \\(X\\) with lognormal, gamma, Pareto or generalized Pareto (for tails). Reinsurance is fundamentally about the tail of \\(X\\) and the accumulation of \\(N\\).
Why it matters for reinsurance
Every layer price, every retention decision and every capital number derives from the distribution of \\(S\\). The rest of this section builds the tools to estimate it: pricing methods, excess-of-loss math, stop-loss and aggregate distributions.
