Pricing Short-Term Insurance Contracts for Exam STAM

Frequency-Severity Framework

Short-term insurance pricing builds on separating claim frequency from claim severity. The pure premium equals expected frequency times expected severity: E[S] = E[N] times E[X]. Common frequency distributions include Poisson, negative binomial, and binomial. Severity distributions include lognormal, Pareto, gamma, and Weibull. This decomposition allows actuaries to model each component independently and apply trend factors, development factors, and credibility adjustments to each.

Premium Components

The gross premium includes the pure premium plus provisions for expenses, profit, and contingencies. Fixed and variable expenses are loaded differently. The expense-loaded premium can be derived using the loss ratio method (premium = expected losses / target loss ratio) or the pure premium method (premium = pure premium + fixed expense per policy, all divided by 1 minus variable expense ratio minus profit margin). Exam STAM tests your ability to combine frequency-severity models with expense loading, and to adjust premiums for policy modifications like deductibles and limits.