Finance AI Skill
Premium Liability Reserving
Calculate and manage insurance premiums, loss reserves, IBNR reserves, and liability estimates for insurance operations or companies with significant warranty/contingent liabilities. Use when pricing insurance products, estimating claim reserves, calculating IBNR, analyzing loss ratios, managing reinsurance arrangements, or preparing statutory financial statements for insurance entities. Triggers on phrases like "loss reserves", "IBNR", "insurance reserves", "claim reserves", "loss ratio", "premium calculation", "actuarial reserve", "unearned premium", "reserve adequacy", "stochastic modeling", "claim frequency", "claim severity".
Premium & Liability Reserving
Calculate insurance premiums, estimate claim reserves (case reserves and IBNR), analyze loss ratios, and ensure reserve adequacy for insurance operations.
Workflow
1. Reserve Estimation Framework
CLAIM RESERVE COMPONENTS
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TOTAL CLAIMS LIABILITY = Case Reserves + IBNR + IBNER
CASE RESERVES (Reported but not paid):
→ Actuarially evaluated per claim
→ Based on claim-specific information
→ Updated by claims adjusters
→ Represents known claims still outstanding
IBNR — Incurred But Not Reported:
→ Claims that have occurred but not yet reported
→ Estimated using statistical methods
→ Varies by line of business, reporting lag
→ Typically 20-50% of total reserves
IBNER — Incurred But Not Enough Reported:
→ Additional development on reported claims
→ Case reserve deficiency
→ Estimated through reserve development analysis
RESERVE ESTIMATION METHODS:
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Method Use Case Accuracy Complexity
──────────────────────────────────────────────────────────────────────────────
Bornhuetter-Ferguson Low development claims HIGH MEDIUM
Chain Ladder Stable, mature book HIGH LOW
Cape Cod (Incurred) New lines, high IBNR MEDIUM MEDIUM
Claims Count Frequency-based estimation MEDIUM LOW
Stochastic Modeling Capital modeling, VaR HIGH HIGH
Kaplan-Meier Tail-heavy lines HIGH HIGH2. Chain Ladder Method
CHAIN LADDER DEVELOPMENT TRIANGLE
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Cumulative Paid Losses by Accident Year and Development Period
(all amounts in $000s)
Accident Year | D+0 | D+1 | D+2 | D+3 | D+4 | D+5 | Ultimate
───────────────┼───────┼────────┼────────┼────────┼────────┼────────┼──────────
2019 | 1,200 | 1,800 | 2,200 | 2,500 | 2,700 | 2,800 | 2,850
2020 | 1,400 | 2,100 | 2,600 | 2,950 | 3,200 | 3,350 | 3,420
2021 | 1,600 | 2,400 | 3,000 | 3,400 | 3,700 | 3,850 | 3,920
2022 | 1,800 | 2,700 | 3,400 | 3,850 | 4,200 | 4,350 | —
2023 | 2,000 | 3,000 | 3,800 | 4,300 | 4,700 | — | —
2024 | 2,200 | 3,300 | 4,200 | 4,800 | — | — | —
DEVELOPMENT FACTORS:
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Calculate link ratios:
D+0→1: avg(1800/1200, 2100/1400, 2400/1600, 2700/1800, 3000/2000, 3300/2200)
= avg(1.50, 1.50, 1.50, 1.50, 1.50, 1.50) = 1.500
D+1→2: avg(2200/1800, 2600/2100, 3000/2400, 3400/2700, 3800/3000)
= avg(1.222, 1.238, 1.250, 1.259, 1.267) = 1.247
D+2→3: avg(2500/2200, 2950/2600, 3400/3000, 3850/3400, 4300/3800)
= avg(1.136, 1.135, 1.133, 1.132, 1.132) = 1.134
D+3→4: avg(2700/2500, 3200/2950, 3700/3400, 4200/3850, 4700/4300)
= avg(1.080, 1.085, 1.088, 1.091, 1.093) = 1.087
D+4→5: avg(2800/2700, 3350/3200, 3850/3700, 4350/4200)
= avg(1.037, 1.047, 1.041, 1.036) = 1.040
D+5→Ult: avg(2850/2800, 3420/3350, 3920/3850)
= avg(1.018, 1.021, 1.018) = 1.019
CUMULATIVE DEVELOPMENT FACTORS:
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From D+0 to:
D+1: 1.500
D+2: 1.500 × 1.247 = 1.871
D+3: 1.871 × 1.134 = 2.122
D+4: 2.122 × 1.087 = 2.306
D+5: 2.306 × 1.040 = 2.398
Ultimate: 2.398 × 1.019 = 2.443
ULTIMATE LOSS PROJECTIONS:
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Accident Year Latest Cum Paid CDF Ultimate Reserve Needed
──────────────────────────────────────────────────────────────────────
2022 $4,350 2.443 $10,627 $6,277
2023 $4,700 2.443 $11,482 $6,782
2024 $4,800 2.443 $11,726 $6,926
──────────────────────────────────────────────────────────────────────
TOTAL IBNR + Outstanding Reserve: $20,085
IBNR = Ultimate - Latest Cumulative Paid
2022 IBNR: $10,627 - $4,350 = $6,277
2023 IBNR: $11,482 - $4,700 = $6,782
2024 IBNR: $11,726 - $4,800 = $6,926
Total IBNR: $19,985
Total Case Reserve (reported claims): $3,500 (from claims data)
Total Claims Liability: $3,500 + $19,985 = $23,4853. Loss Ratio Analysis
LOSS RATIO ANALYSIS
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Loss Ratio = Incurred Losses / Earned Premium
Expense Ratio = Underwriting Expenses / Written Premium
Combined Ratio = Loss Ratio + Expense Ratio
BREAKDOWN BY LINE OF BUSINESS — FY 2024:
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Line of Business Earned Prem Incurred Loss Loss Ratio Expense R Combined
($000s) ($000s) (%) (%) Ratio
────────────────────────────────────────────────────────────────────────────────────
Property $12,000 $8,400 70.0% 22.0% 92.0%
General Liability $8,500 $5,950 70.0% 24.0% 94.0%
Workers' Comp $6,000 $4,500 75.0% 20.0% 95.0%
Auto (Commercial) $7,500 $5,625 75.0% 23.0% 98.0%
Cyber Liability $3,000 $2,100 70.0% 28.0% 98.0%
Professional Liab $4,000 $2,400 60.0% 26.0% 86.0%
────────────────────────────────────────────────────────────────────────────────────
TOTAL $41,000 $29,025 70.8% 23.2% 94.0%
INTERPRETATION:
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Combined Ratio < 100%: Underwriting profit
Combined Ratio > 100%: Underwriting loss (rely on investment income)
Performance by line:
→ Property: 92.0% — GOOD ✓
→ General Liability: 94.0% — GOOD ✓
→ Workers' Comp: 95.0% — ACCEPTABLE ✓
→ Auto (Commercial): 98.0% — THIN ⚠ (review pricing adequacy)
→ Cyber Liability: 98.0% — THIN ⚠ (emerging risks, monitor development)
→ Professional Liab: 86.0% — EXCELLENT ✓
TREND ANALYSIS (3-year combined ratio trend):
Auto (Commercial): 96.0% → 97.5% → 98.0% — WORSENING ⚠
Cyber Liability: 94.0% → 96.5% → 98.0% — WORSENING ⚠
Property: 93.5% → 92.5% → 92.0% — IMPROVING ✓
RECOMMENDATIONS:
→ Auto: Increase rates 5-8% on renewal book
→ Cyber: Reprice new business; tighten underwriting guidelines
→ Property: Maintain current pricing; consider expanding capacity4. Premium Calculation & Pricing
PREMIUM CALCULATION FRAMEWORK
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Expected Loss Premium = Exposure Unit × Loss Cost Rate
Example — Commercial Auto Policy:
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RATING FACTORS:
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Base rate (per $100K coverage): $450
Territory factor (Region B): 1.15
Experience modifier (prior losses): 0.90
Driver rating (fleet size 10-25): 1.10
Coverage limits (1M/2M): 1.30
Deductible ($1,000): 1.00
Policy period (annual): 1.00
GROSS PREMIUM = $450 × 1.15 × 0.90 × 1.10 × 1.30 × 1.00 × 1.00
= $707 per $100K coverage
= $7,070 for $1M coverage
NET PREMIUM (after discounts):
→ Multi-policy discount (5%): ($354)
→ Loyalty discount (3%): ($212)
→ Payment plan surcharge (1%): $71
→ ──────────────────────────────────
NET PREMIUM: $6,575
EXPECTED LOSS COST:
→ Historical loss ratio: 75%
→ Expected losses: $6,575 × 75% = $4,931
→ Expected expense: $6,575 × 23% = $1,512
→ Expected underwriting profit: $6,575 - $4,931 - $1,512 = $132 (2.0%)
REINSURANCE COST:
→ Excess of loss treaty: $500K deductible, $2M limit
→ Reinsurance premium: $420
→ Net premium after reinsurance: $6,155
→ Net retention premium: $6,155 - $420 = $5,7355. Reserve Adequacy Testing
RESERVE ADEQUACY ANALYSIS — Q4 2024
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CURRENT RESERVES:
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Line of Business Case Reserve IBNR Reserve Total Reserve Latest
($000s) ($000s) ($000s) Est.
─────────── ──────────── ─────────── ──────
Property $2,500 $5,200 $7,700 $7,500
General Liability $1,800 $3,600 $5,400 $5,600
Workers' Comp $1,200 $2,100 $3,300 $3,200
Auto (Commercial) $1,500 $3,200 $4,700 $5,100
Cyber Liability $400 $1,100 $1,500 $1,700
Professional Liab $600 $1,000 $1,600 $1,500
────────────────────────────────────────────────────────────────────
TOTAL $8,000 $16,200 $24,200 $24,600
ADEQUACY ASSESSMENT:
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Line Current Latest Est. Difference Action
Reserve Reserve
─────────────────────────────────────────────────────────────────
Property $7,700 $7,500 +$200 Adequate ✓
General Liability $5,400 $5,600 ($200) +$200 needed
Workers' Comp $3,300 $3,200 +$100 Adequate ✓
Auto (Commercial) $4,700 $5,100 ($400) +$400 needed ⚠
Cyber Liability $1,500 $1,700 ($200) +$200 needed ⚠
Professional Liab $1,600 $1,500 +$100 Adequate ✓
─────────────────────────────────────────────────────────────────
TOTAL $24,200 $24,600 ($400) +$400 needed
RESERVE STRENGTHENING REQUIRED: $400K
→ Auto (Commercial): +$400K (worsening loss trend, inadequate case reserves)
→ General Liability: +$200K (IBNR development, tail risk)
→ Cyber Liability: +$200K (emerging cyber risk claims, higher severity)
JOURNAL ENTRY:
Dr Loss Expense $800,000
Cr Loss Reserve — Auto $400,000
Cr Loss Reserve — Gen Liability $200,000
Cr Loss Reserve — Cyber $200,000
NOTE: Total $800K but $400K already partially accrued; net additional $400KEdge Cases
- Tail risk: Long-tail lines (professional liability, cyber) require longer development periods
- Catastrophe events: Natural disasters cause reserve spikes; model catastrophe exposure separately
- Litigation environment: Jurisdiction-specific adjustments for legal environments
- Regulatory changes: New statutory reserve requirements may mandate changes
- Reinsurance disputes: Recoverable from reinsurer vs ceded reserves
Integration Points
- Claims management systems: Guidewire, Duck Creek, ClaimCenter
- Actuarial software: R, Prophet, AXIS, MSS
- Rating engines: Premium calculation systems
- Reinsurance systems: Treaty tracking, claims recovery
- Statutory reporting: NIHP, statutory financial statements
- Capital models: Risk-based capital (RBC), Solvency II
Output
Reserve Report
CLAIM RESERVE REPORT — Q4 2024
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Total reserves held: $24,200K
→ Case reserves: $8,000K (33%)
→ IBNR reserves: $16,200K (67%)
Reserve adequacy:
→ Adequate: 4 of 6 lines
→ Strengthening needed: $400K
→ Lines requiring action: Auto, Gen Liability, Cyber
Combined ratio: 94.0% (underwriting profit achieved)
→ Loss ratio: 70.8%
→ Expense ratio: 23.2%
Recommendation: Strengthen reserves by $400K; increase auto and cyber rates on renewalDisclaimer: All rights reserved by Circulos AI. These skills are specifically designed for Claude Code, Claude Cowork, Codex, and OpenClaw. When using or referencing any skill, please provide proper attribution to Circulos AI.