The primary tool for reserving is the loss development triangle. It arrays cumulative incurred losses by accident period (rows) and development period (columns, e.g., 12-month intervals).
Example (simplified, $ millions):
| Accident Year | 12 Months | 24 Months | 36 Months | 48 Months | | :--- | :--- | :--- | :--- | :--- | | 2023 | 100 | 180 | 210 | 220 | | 2022 | 110 | 200 | 235 | ? | | 2021 | 105 | 195 | ? | ? | | 2020 | 115 | ? | ? | ? |
The triangle shows that as a claim cohort ages, losses increase (develop). The actuary’s goal is to project the final diagonal (ultimate losses) using historical development patterns. The primary tool for reserving is the loss
Ratemaking and loss reserving are the dual pillars of P&C insurance solvency. Reserving looks backward to estimate what is owed from the past; ratemaking looks forward to set the price for future risk. While the Chain Ladder and Pure Premium methods remain industry workhorses, the actuary must supplement them with judgmental adjustments for trends (social inflation, technology), credibility weighting, and regulatory constraints (IFRS 17, state prior-approval laws). Ultimately, the art of P&C actuarial science lies in balancing historical data with forward-looking assumptions in a world where the ultimate cost of a policy is known only after it has expired.
Scenario: An actuary is analyzing Auto Liability data for Accident Year 2023.
Ratemaking Phase:
Reserving Phase:
Both ratemaking and reserving revolve around the fundamental insurance equation:
$$Premium = Losses + Expenses + Profit$$ Scenario: An actuary is analyzing Auto Liability data
Where:
If the premium is set too low (Ratemaking error) or the liabilities are underestimated (Reserving error), the insurer risks insolvency.