Insurance quantities and the prediction problem
Begin every analysis by defining the insurance quantity being predicted and the decision it will support. Claim count, claim severity, aggregate loss, probability of fraud, renewal, and outstanding claim liability are different targets. Their units, observation windows, and available predictors differ. A model of claim frequency does not directly predict the average payment per claim. A model of reported claims may not describe ultimate incurred losses. State the target precisely before selecting an algorithm or calculating an apparent improvement.
Exposure measures the amount of risk observed. Depending on the line and purpose, it may involve insured time, payroll, sales, or another justified base. For a simple frequency calculation, divide the relevant claim count by the corresponding exposure. For average severity, divide the corresponding loss amount by the relevant claim count. Their product gives pure premium when the definitions and populations are compatible. Keep deductibles, limits, recoveries, expenses, and the treatment of zero claims consistent. Mixing a net loss numerator with an incompatible gross exposure or count can create a misleading result.
Insurance records mature over time. Claims can be reported after the loss event, and reported claims can develop as information or payments change. Paid loss, case reserves, incurred loss, and an estimate of ultimate loss are related but distinct quantities. An apparent improvement in a recent accident period may reflect immaturity rather than better underlying experience. Development and trend address different phenomena: development concerns emergence toward an ultimate estimate, while trend concerns changes in cost or frequency across time. Neither should be mechanically substituted for the other.
For pricing, distinguish expected claim cost from the premium needed after considering expenses, profit, risk, and other relevant constraints. A model relativity is not automatically a legally permissible or operationally appropriate rating factor. For reserving, uncertainty in future claim development is not removed by a precise fitted value. For fraud investigation, a high model score is a signal for review, not a finding that a particular person committed fraud. Match interpretation and action to the actual analytical objective.
The CSPA catalog title refers to the CAS Institute credential, whose official requirements span insurance foundations, data concepts, predictive modeling, ethics, and a practical project. This practice page combines foundations across those areas and is not a replacement for the relevant component's current syllabus or software work. It also does not represent the separate CAS PCPA assessment. In a numerical problem, write the units beside each calculation. In a business problem, explain which population, observation period, information date, and decision make the result meaningful.