Loss Reserve Analysis

• Is this paid losses, incurred losses, or both?
• What is the evaluation date?
• Are the development periods in months or years?
• Is there an earned premium column or sheet for BF/Cape Cod methods?

Per ASOP No. 23 (Data Quality), Section 3.2 (Selection of Data), consider whether the data is appropriate for the intended analysis. Ask the user about known data issues such as changes in claim coding, coverage triggers, or reopened claims that may affect triangle integrity. See Friedland Ch. 1–4 for background on the claims process, data types, and meeting with management to understand context.

Supported formats:

• Standard triangle layout: rows = accident years/quarters, columns = development periods
• Columnar layout: columns for accident period, development period, and loss amount
• Transaction-level data: claim-level records with accident_date, evaluation_date, and loss amounts — automatically aggregated into a triangle
• Schedule P format (will need manual identification of the relevant section)

Sample data (in examples/) for testing all methods:

• sample_triangle.csv — 5×5 paid loss triangle (2019-2023)
• sample_loss_transactions.csv — ~500 claims with paid, case reserve, and incurred columns
• sample_premium.csv — earned premium by accident year (enables BF and Cape Cod methods)

Step 2: Run the Analysis

Execute the main analysis script:

python scripts/reserve_analysis.py \
  --input <path_to_triangle_file> \
  --sheet <sheet_name_if_excel> \
  --type <paid|incurred|both> \
  --dev-periods <months|years> \
  --premium <path_or_value_if_available> \
  --output /home/claude/reserve_report.xlsx

The script runs these methods:

1. Chain Ladder (Volume-Weighted) — Standard link ratio method using volume-weighted average factors (Friedland Ch. 7; foundational development method per ASOP No. 43 Section 3.6.1)
2. Chain Ladder (Simple Average) — Arithmetic average of age-to-age factors for comparison
3. Bornhuetter-Ferguson — If earned premium is provided; blends expected loss ratio with chain ladder (Friedland Ch. 9; Bornhuetter & Ferguson, PCAS 1972; incorporates credibility concepts per ASOP No. 25)
4. Cape Cod — If earned premium is provided; derives expected loss ratio from the data itself (Friedland Ch. 10; Stanard, PCAS 1985)
5. Expected Loss Ratio — If earned premium and an a priori loss ratio are provided (Friedland Ch. 8; useful when development data has limited credibility per ASOP No. 43 Section 3.6.1)

Step 3: Review Diagnostics

The script also produces diagnostic exhibits. Review these and call out to the user:

• Calendar year development test: Checks if development along diagonals is consistent. Large swings may indicate reserve strengthening/weakening or operational changes.
• High/low factor analysis: Flags individual age-to-age factors that are outliers (>2 standard deviations from the mean for that development period).
• Tail factor sensitivity: Shows how ultimates change under ±10% and ±25% tail factor variations.
• Incurred-vs-paid gap (if both triangles provided): Large divergence in later maturities may signal case reserve adequacy issues.
• Residual plots: Standardized residuals from the chain ladder model to check for systematic patterns.

These diagnostics align with ASOP No. 43 Section 3.7.1 (Reasonableness), which calls for the actuary to assess whether results are reasonable. The calendar year test and outlier analysis help identify data irregularities referenced in ASOP No. 23 Section 3.3 (Review of Data). See also Friedland Ch. 6 for discussion of the development triangle as a diagnostic tool and Werner & Modlin Ch. 6 for loss development context in ratemaking.

Step 4: Rebuild Workbook with Formula Transparency

The script produces a workbook with static values. Before presenting, rebuild the workbook so every derived cell uses a live Excel formula with a cached calculated value. This is the minimum transparency standard for actuarial work — a reviewer must be able to click any cell and trace the calculation back to the source triangle.

What must be a formula (not a static value):

• Individual age-to-age factors: =TriangleCell[next_dev] / TriangleCell[current_dev]
• Volume-weighted averages: =SUM(next_col_range) / SUM(current_col_range)
• Simple averages: =AVERAGE(factor_range)
• Medial averages: =(SUM(range)-MIN(range)-MAX(range))/(COUNT(range)-2) when count >= 3
• Selected factors: reference to the corresponding average row
• CDF chain: =SelectedATA * CDF_next_period (right-to-left multiplication)
• % Reported: =1/CDF
• Latest loss: reference to the diagonal cell on the triangle sheet
• Chain ladder ultimate: =LatestLoss * CDF
• IBNR: =Ultimate - LatestLoss
• BF % unreported: =1 - %Reported
• BF IBNR: =ELR * Premium * %Unreported
• BF/CC ultimate: =LatestLoss + IBNR
• Cape Cod derived ELR: =SUM(LatestLoss_range) / SUMPRODUCT(Premium_range, %Reported_range)
• All totals: =SUM(range)
• Summary sheet: cross-sheet references to the CL Ultimates and BF/Cape Cod sheets
• Tail factor derivation (on the ATA sheet, below the CDF rows). Build this block so a reviewer can trace exactly how the tail was derived:
  • List the last 3–5 selected ATA factors where factor > 1.0 in a small table with columns:
    • Development Period (static label)
    • Selected ATA (formula reference to the Selected row above)
    • Excess: =ATA_cell - 1
    • LN(Excess): =LN(excess_cell)
  • Slope: =INDEX(LINEST(ln_excess_range, period_range), 1, 1)
  • Intercept: =INDEX(LINEST(ln_excess_range, period_range), 1, 2)
  • Projected excess for each extrapolated period beyond the triangle: =EXP($slope_cell * period + $intercept_cell) — extend rows until projected < 0.0001 or max 20 extra periods
  • Projected ATA for each: =1 + projected_excess_cell
  • Tail factor: =PRODUCT(projected_ATA_range)
  • Guard condition: if slope >= 0 or fewer than 3 qualifying factors, set tail = 1.000 with a note explaining why (no decay detected or insufficient data)
  • The CDF chain's rightmost value must reference this tail factor cell, not a hardcoded number

What stays as static values (inputs, not derived):

• Triangle data (raw input)
• Earned premium (user input)
• A priori ELR for BF (user input or derived assumption)
• Diagnostics sheet (calendar year test, outliers, tail sensitivity — complex stats)

Important: Every formula cell must also have a cached calculated value so numbers display correctly in all viewers (web preview, Excel, Google Sheets). Use xlsxwriter's write_formula(row, col, formula, format, result) or equivalent approach that writes both the formula and the pre-calculated value.

Step 5: Interpret Results and Present

After running the analysis:

1. Copy the output Excel to /mnt/user-data/outputs/
2. Present the file to the user
3. Provide a narrative summary that includes:
   • The range of indicated ultimates across methods
   • Whether carried reserves appear adequate, deficient, or redundant relative to the chain ladder indication
   • Which accident years show the most development volatility
   • Any red flags from the diagnostics
   • Caveats about data limitations and the quick-check nature of the analysis
   • Reference the concept from ASOP No. 43 Section 3.7 (Unpaid Claim Estimate) and 3.7.1 (Reasonableness) — note that a point estimate is a selection, and the actuary should assess whether results are reasonable

Important tone guidance: This is a quick check, not a full reserve study. Always caveat that:

• The analysis relies on standard methods and does not incorporate claim-level information
• Tail factor selection is mechanical and should be reviewed by a credentialed actuary
• Results should be cross-referenced with operational knowledge (e.g., changes in claims handling, coverage, or legal environment)
• This does not constitute an actuarial opinion under ASOP No. 43 or a Statement of Actuarial Opinion per ASOP No. 36. A credentialed actuary should review results, apply professional judgment on factor selections, and consider the requirements of ASOP No. 43 Section 3 before relying on these estimates for decision-making

Step 5: Interactive Follow-Up

After presenting results, offer the user options to:

• Adjust tail factors manually
• Exclude specific accident years or development periods
• Change the weighting scheme for age-to-age factors
• Run sensitivity scenarios on the a priori loss ratio (for BF/Cape Cod)
• Compare against a benchmark loss ratio

When adjusting selections, note that ASOP No. 43 Section 3.6.7 (Changing Conditions) and 3.6.6 (External Conditions) may affect development patterns and tail behavior. ASOP No. 25 provides guidance on credibility weighting when blending methods. Tail factor considerations are discussed in Friedland Ch. 7 as part of the development technique.

Key Actuarial Concepts (Reference)

Read references/methods.md for detailed formulas and implementation notes on each method if needed during development or debugging.

Error Handling

• If the triangle has fewer than 3 accident periods, warn that credibility is very limited. ASOP No. 25 Section 3.4 (Professional Judgment) notes that credibility assessment is not always a precise mathematical process; triangles with very few data points may warrant heavier reliance on the ELR or BF methods with an externally-derived expected loss ratio
• If any development factors are < 1.0 (negative development), flag explicitly — it may be legitimate but warrants explanation
• If the triangle is not square (jagged), handle gracefully by only computing factors where data exists
• If earned premium is not provided, skip BF and Cape Cod methods and note this in the output