Chapter 15 Loss Reserving Methods

Loss reserves are estimates representing future loss and expense payments and constitute a major portion of an insurer's liabilities.
Accurate reserving is critical for insurer stability, solvency, and determining policyholders’ surplus.
Incurred losses are calculated using the formula: $\text{Incurred losses} = \text{Paid losses} + \text{Loss reserves} + \text{Loss adjustment expense reserves}$
The accident-year method aggregates all incurred losses for events occurring within a specific twelve-month period, regardless of when claims are reported or paid.
Loss development refers to the change in incurred losses over time as new information becomes available.

The National Association of Insurance Commissioners (NAIC) categorizes LAE as:
- Defense and Cost Containment (DCC): Expenses related to litigation and defense.
- Adjusting and Other (AO): All other expenses, including adjusters' salaries.
Actuarial literature frequently uses legacy terms:
- Allocated Loss Adjustment Expense (ALAE): Expenses directly associated with a specific claim.
- Unallocated Loss Adjustment Expense (ULAE): Overall claim operation expenses not linked to individual files.

Policyholders’ surplus represents an insurer’s net worth: $\text{Surplus} = \text{Assets} - \text{Liabilities}$
Underreserving overstates policyholders’ surplus and underwriting profit, potentially leading to insolvency.
Overreserving understates surplus and may lead to unwarranted rate increases or tax penalties on deferred income.
Reserves must account for the ultimate settlement value of a claim rather than its present value.

Judgment Method: A claims representative estimates the value based on professional experience with similar claims without statistical analysis.
Average Method (Factor Method): Assigns an average reserve amount to specific categories of frequent, low-variation claims based on past data trended for inflation.
Tabular Method: Uses actuarial tables (considering age, health, and marital status) to calculate the present value of future benefits, such as workers compensation lost income.
Additional Case Reserves: A percentage added to existing case reserves to correct for anticipated development in reported losses.

Incurred But Not Reported (IBNR) reserves cover unknown future payments for losses that have occurred but are not yet reported, including those expected to exceed current reserves (IBNER).
IBNR calculation: $\text{IBNR reserves} = \text{Ultimate losses} - \text{Reported incurred losses}$
Loss Ratio Method: Assumes the ultimate loss ratio equals the ratio used when calculating premium rates; used mainly in the first $1$ to $2$ years of development.
Percentage Method: Uses historical relationships between IBNR and reported losses to forecast future development.
Loss Triangle Method (Chain Ladder): Uses historical data (link ratios) to project future development. Key steps include:
1. Organizing data into a triangle format.
2. Calculating twelve-month loss development factors.
3. Calculating ultimate loss development factors.
4. Applying ultimate factors to current incurred losses.

Two-Part Combination: A weighted average of the loss ratio and loss triangle methods.
Bornhuetter-Ferguson Method: Estimates IBNR by using expected losses and an IBNR factor; useful when data is immature or for reinsurers facing reporting delays.
Three-Part Combination: Phases through three weights:
- Initial stage: Emphasis on the loss ratio method.
- Intermediate stage: Emphasis on the loss triangle method.
- Final stage: Emphasis on case loss reserves.

Reinsurers rely on the primary insurer's data; pro rata reinsurers follow primary reserving practices exactly.
Excess of loss reinsurers face greater uncertainty due to the attachment point (retention) and significant time lags.
Monetary and social inflation disproportionately affect excess of loss layers by increasing both the number and the value of claims exceeding retentions.
Salvage (sale of transferred property) and Subrogation (recovery from legally responsible third parties) are treated as offsets to loss reserves and reductions to paid losses in NAIC Schedule P.