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Expected Claims

Note Section 1.2 • Reading time: ~5 mins

The Expected Claims (or Expected Loss Ratio) reserving method estimates ultimate losses based on an a priori expectation of losses, completely ignoring historical loss development to date for the subject period.

Key Assumptions

  • Independence of Development: The cumulative claims observed to date do not provide useful information about the ultimate cost of unpaid claims.
  • A Priori Estimation: The selected Expected Loss Ratio (ELR) or Expected Pure Premium is a stable, representative measure of the risk profile.

Mathematical Formulation

The ultimate losses for a given accident year are:

Ultimate Losses=Earned Premium×Expected Loss Ratio\text{Ultimate Losses} = \text{Earned Premium} \times \text{Expected Loss Ratio}

Alternatively, utilizing exposures (EE):

Ultimate Losses=E×Expected Pure Premium\text{Ultimate Losses} = E \times \text{Expected Pure Premium}

Unpaid Claims and IBNR

The unpaid claim estimate is:

Unpaid Claims=Ultimate Losses−Paid Losses\text{Unpaid Claims} = \text{Ultimate Losses} - \text{Paid Losses}

IBNR (Incurred But Not Reported) is:

IBNR=Ultimate Losses−Reported Losses\text{IBNR} = \text{Ultimate Losses} - \text{Reported Losses}

[!WARNING] Common Reserving Mistake Paid losses must be subtracted from ultimate losses to calculate unpaid claims (reserve liability). Subtracting reported losses calculates IBNR specifically. Do not confuse the two.

Selecting the Expected Loss Ratio (ELR)

  • Historical Data Selection: The ELR should be derived from historical, mature years. Actuaries must not include the experience period being evaluated in the ELR calculation, as doing so would violate the independence assumption.
  • On-Leveling and Trending: Historical premiums must be on-leveled to the current rate level, and both premiums and losses must be trended to the future period to ensure consistency.

When to Use the Expected Claims Method

This method is particularly suitable in the following scenarios:

  1. New Lines of Business: Where no historical development triangles exist for the specific book.
  2. Immature Evaluation Ages: In long-tailed lines at early maturities where Chain Ladder projections are highly volatile.
  3. High-Severity, Low-Frequency Lines: Where development is erratic and prone to large reporting lags.
  4. Operational Disruptions: When claims processing or case reserving practices have changed significantly, rendering historical development patterns unreliable.

Actuarial Diagnostics: Negative IBNR

Negative IBNR occurs when the selected ultimate losses are less than current reported losses (IBNR=Ultimate Losses−Reported Losses<0\text{IBNR} = \text{Ultimate Losses} - \text{Reported Losses} < 0). This may occur due to:

  • Conservative Case Reserves: Claim adjusters (the individuals setting case reserves) setting case outstanding estimates too high initially.
  • Anticipated Recoveries: Expectations of significant future salvage or subrogation recoveries.