Introduction To Ratemaking And Loss Reserving For Property And Casualty Insurance

  • Select LDFs: Actuaries select an average (simple, weighted, or geometric) of these factors.
  • Cumulative Development Factors (CDF): Multiply the factors cumulatively to reach "Ultimate."
  • Estimate Ultimate Loss: $$Ultimate\ Loss = Reported\ Loss \times CDF$$
  • Calculate Reserve: $$Reserve = Ultimate\ Loss - Reported\ Loss$$

    • To deepen your knowledge:

  • Practice: Obtain a public NAIC annual statement and attempt to calculate a simple chain-ladder for a single accident year.

    • End of Content Introduction

    | Term | Definition | | :--- | :--- | | Ultimate Loss | Total final amount an insurer will pay for a group of claims. | | Loss Ratio | (Incurred Losses) / (Earned Premiums) – A profitability measure. | | Combined Ratio | Loss Ratio + Expense Ratio. >100% = Underwriting loss. | | Adverse Development | When actual losses turn out higher than reserved amounts. | | Discounting | Reducing reserves to present value (allowed for long-tail lines like workers' comp). | | ALAE (Allocated Loss Adjustment Expense) | Legal, investigation costs directly tied to a specific claim. | Select LDFs: Actuaries select an average (simple, weighted,

    Actuaries use historical patterns to project future outcomes. The three most common methods are:

    1. The Chain Ladder (or Development) Method This is the industry workhorse. It uses a loss development triangle—a matrix of cumulative claim payments or incurred losses by accident year and development age. To deepen your knowledge:

    Example: For Accident Year 2023, after 12 months you have paid $1M. The average 12→24 month development factor is 1.20. The 24→36 month factor is 1.05. The projected ultimate loss = $1M × 1.20 × 1.05 = $1.26M. Reserve = $1.26M - Amount Paid to Date.

    2. The Bornhuetter-Ferguson (B-F) Method The chain ladder trusts the data entirely. The B-F method distrusts early data and blends an expected loss ratio (from pricing) with observed development. It is excellent for new, volatile accident years where paid data is sparse. Practice: Obtain a public NAIC annual statement and

    3. Expected Claims Method Used when historical data is unreliable (e.g., a new product line). The reserve is simply:

    Expected ultimate loss = Earned Premium × Expected Loss Ratio Reserve = Expected Ultimate Loss – (Paid Loss + Case Reserves)

    Loss Reserving (or Loss Development) is the process of estimating the liability for unpaid claims on the balance sheet. This is crucial for solvency.