What is rate-on-line (ROL) in reinsurance?

Rate-on-line (ROL) is the reinsurance premium expressed as a percentage of the treaty limit (maximum payout). If a catastrophe excess-of-loss treaty has a $100M limit and the annual premium is $8M, the ROL is 8%. ROL allows comparison across treaties with different limits. The inverse of ROL is the payback period — at 8% ROL, the reinsurer earns back the full limit in 12.5 years of premium, absent losses. ROL is compared to the expected loss ratio (ELR) and required combined ratio to assess profitability.

What is the difference between proportional and non-proportional reinsurance?

In proportional reinsurance (quota share, surplus share), the reinsurer shares a percentage of both premiums and losses. In a 30% quota share, the reinsurer receives 30% of premiums and pays 30% of all losses plus a ceding commission. In non-proportional reinsurance (excess of loss), the reinsurer only pays losses above a retention threshold (the attachment point) up to the treaty limit, in exchange for a fixed premium (ROL × limit).

AI for Reinsurance Pricing: Catastrophe Modeling, Rate-on-Line, and Treaty Analysis with Claude (2026)

How reinsurance underwriters and actuaries use Claude AI for treaty pricing: burning cost calculation with trend and development adjustments, catastrophe loading from cat model outputs, quota share vs excess-of-loss structure analysis, and cedant portfolio adverse selection review.

Reinsurance Pricing and AI

Reinsurance pricing requires synthesizing catastrophe model outputs, historical loss development, cedant portfolio data, and market conditions into an actuarially supported rate recommendation. Claude with ClaudeFinLab structures the pricing analysis — from burning cost calculation to catastrophe loading to ROL benchmark comparison — helping reinsurance underwriters and actuaries produce faster, documented pricing packages.

Burning Cost Pricing

"Compute the burning cost for an excess-of-loss property treaty: Layer: $10M xs $5M (pays losses between $5M-$15M per occurrence). 10-year historical loss data: Year 1: $2.4M layer loss; Year 2: $0; Year 3: $0; Year 4: $8.7M; Year 5: $0; Year 6: $1.2M; Year 7: $0; Year 8: $0; Year 9: $14.9M; Year 10: $3.1M. Total layer losses: $30.3M over 10 years. Average annual layer loss (burning cost): $3.03M. Exposed subject premium (cedant's underlying premium) $45M/year. Burning cost ratio: $3.03M / $45M = 6.73%. As a ROL on the $10M layer: $3.03M / $10M = 30.3%."
"Apply trend and development adjustments to the burning cost: (1) Loss trend: 5% per year (inflation + social inflation). Apply trend factor to each year: Year 1 losses × 1.05^9 (9 years of trend), Year 2... etc. Trended average annual loss: $4.12M. (2) Premium trend: 8% annual premium growth (cedant's book grew). Re-state each year's burning cost ratio on a premium-trended basis. (3) IBNE loading: 10% (incurred but not enough reserves). Final trended/developed burning cost: $4.53M/year. ROL indication: $4.53M / $10M = 45.3%."

Catastrophe Loading

"Add catastrophe loading to the burning cost: the burning cost captures attritional losses but not infrequent catastrophes. Catastrophe modeling output (RMS/AIR): 100-year return period loss to this layer: $8.2M. 250-year: $9.6M (near limit). Expected catastrophe loss (probability-weighted): 1/100 × $8.2M + 1/250 × $9.6M = $82K + $38K = $120K/year from catastrophe scenarios. But historical data already captures some cat events (Year 9 loss may be cat-related). Cat loading: $120K/year on top of trended burning cost. Total indicated rate: ($4.53M + $0.12M) / $10M = 46.5% ROL."

Quota Share Treaty Analysis

"Analyze a 40% quota share treaty for a liability cedant: cedant cedes 40% of all premiums and losses. Subject premium $85M. Ceded premium: $34M. Ceding commission: 30% of ceded premium = $10.2M (reinsurer pays this back to cedant). Net premium to reinsurer: $34M - $10.2M = $23.8M. Cedant's historical loss ratio: 68%. Expected ceded losses: $85M × 68% × 40% = $23.1M. Reinsurer's expected combined ratio: ($23.1M losses + $10.2M ceding commission) / $34M gross premium = 98%. Expenses: 8%. Total combined: 106% — underwriting loss. What ceding commission level makes the treaty profitable at 95% combined?"

Portfolio Cedant Review

"Review this cedant's portfolio for adverse selection risk before writing the quota share: cedant writes commercial auto liability (60%), GL (25%), umbrella (15%). Social inflation trends: (1) commercial auto verdicts averaging $3.2M in FL/TX/CA (nuclear verdict jurisdictions — 42% of cedant's premium); (2) cedant's loss ratio has trended from 65% (Year 1) to 78% (Year 5) — 13 point deterioration; (3) heavy concentration in trucking (30% of auto premium) — elevated severity. Red flags for the reinsurer: adverse loss trend, geographic concentration in nuclear verdict states, trucking exposure. Price accordingly or seek exclusions."

Where to Start

Paste the cedant's 5-10 year historical loss data for the specific treaty layer and ask Claude to compute the burning cost, apply trend factors (you specify the trend assumptions), and convert to a ROL indication. Then separately input the catastrophe model outputs to compute the cat loading. Comparing your ROL indication against the cedant's requested rate shows whether the deal is priced adequately — the core of the reinsurance underwriting decision.

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