Treaty economics at the speed of conversation.
With receipts.

Ask in plain English. Get a number that stands up to your broker, your actuary, and the underwriting committee.

01 The demo
Watch it run, right here. Tap a prompt, then hit Ask ↓
Payback period, $5M excess layer open ▾
TrueMath
Public Library ▾
···
We're quoting a $5M excess layer. The basic limits loss cost…
▤ Reinsurance Treaty Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
We're quoting a $5M excess layer. The basic limits loss cost is $250,000, the ILF at the attachment is 1.85, and the ILF at the policy limit is 2.60. What's the payback period on this layer?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
xl_layer_limit: 5000000 USD
basic_limits_loss_cost: 250000 USD
ilf_at_retention: 1.85
ilf_at_policy_limit: 2.60
calculate: xl_payback_period yr
↑ This prompt is loaded and ready. Hit Ask to watch TrueMath work.
Jul 9, 2026 3:04 PMResponse
Creating Scenario 1.

Layer ILF

Calculates the ILF for a specific XL layer as the difference in ILFs at the policy limit and retention, normalized to the basic limit ILF.
• ILF at Policy Limit: 2.6000
• ILF at Retention: 1.8500
• ILF at Basic Limit: 1.0000
• Layer ILF: 0.7500

Layer Loss Cost

Calculates the expected loss cost for an XL layer by applying the layer ILF to the basic limits loss cost.
• Basic Limits Loss Cost: $250,000
• Layer ILF: 0.7500
• Layer Loss Cost: $187,500

Indicated Rate on Line

Calculates the indicated rate on line (ROL) for an XL layer: layer loss cost rate plus reinsurer expense ratio and profit load.
• Layer Loss Cost: $187,500
• XL Layer Limit: $5,000,000
• Reinsurer Expense Ratio: 12.000%
• Reinsurer Profit Load: 5.000%
• Indicated Rate on Line: 4.5181%

XL Layer Premium

Calculates the reinsurance premium for an XL layer by applying the ROL to the layer limit.
• Indicated Rate on Line: 4.5181%
• XL Layer Limit: $5,000,000
• XL Layer Premium: $225,904

XL Layer Payback Period

Calculates the number of loss-free years required to pay back a total loss in the XL layer.
• XL Layer Limit: $5,000,000
• XL Layer Premium: $225,904
• XL Layer Payback Period: 22.13 yr
Requested result for XL Layer Payback Period is 22.13 yr.
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UW profit, 30% quota share open ▾
TrueMath
Public Library ▾
···
On a 30% quota share, the cedent writes $40M subject premium…
▤ Reinsurance Treaty Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
On a 30% quota share, the cedent writes $40M subject premium with $21M in losses and we're paying 30% ceding commission. What's our underwriting profit on the treaty?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
quota_share_cession: 30%
subject_premium: 40000000 USD
subject_losses: 21000000 USD
ceding_commission_rate: 30%
calculate: treaty_underwriting_profit
↑ This prompt is loaded and ready. Hit Ask to watch TrueMath work.
Jul 9, 2026 3:05 PMResponse
Creating Scenario 1.

Ceded Premium (Quota Share)

Calculates the ceded premium under a quota share treaty.
• Subject Premium: $40,000,000
• Quota Share Cession: 30.000%
• Ceded Premium: $12,000,000

Sliding-Scale Ceding Commission Amount

Calculates the dollar amount of sliding-scale ceding commission paid to the cedent.
• Ceding Commission Rate: 30.000%
• Ceded Premium: $12,000,000
• Sliding-Scale Ceding Commission Amount: $3,600,000

Ceded Losses (Quota Share)

Calculates the ceded losses under a quota share treaty.
• Subject Losses: $21,000,000
• Quota Share Cession: 30.000%
• Ceded Losses: $6,300,000

Treaty Underwriting Profit

Calculates the reinsurer's underwriting profit on the treaty.
• Ceded Premium: $12,000,000
• Ceded Losses: $6,300,000
• Sliding-Scale Ceding Commission Amount: $3,600,000
• Reinsurer Expense Ratio: 12.000%
• Treaty Underwriting Profit: $660,000
Requested result for Treaty Underwriting Profit is $660,000.
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Combined ratio breakdown, 30% QS open ▾
TrueMath
Public Library ▾
···
Show me the combined ratio breakdown on a 30% quota share where…
▤ Reinsurance Treaty Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
Show me the combined ratio breakdown on a 30% quota share where the cedent writes $40M subject premium against $21M in losses, with a 30% ceding commission.
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
quota_share_cession: 30%
subject_premium: 40000000 USD
subject_losses: 21000000 USD
ceding_commission_rate: 30%
calculate: combined_ratio_waterfall
↑ This prompt is loaded and ready. Hit Ask to watch TrueMath work.
Jul 9, 2026 4:06 PMResponse
Creating Scenario 1.

Ceded Premium (Quota Share)

Calculates the ceded premium under a quota share treaty.
• Subject Premium: $40,000,000
• Quota Share Cession: 30.000%
• Ceded Premium: $12,000,000

Ceded Losses (Quota Share)

Calculates the ceded losses under a quota share treaty.
• Subject Losses: $21,000,000
• Quota Share Cession: 30.000%
• Ceded Losses: $6,300,000

Reinsurer Loss Ratio

Calculates the reinsurer's loss ratio on the treaty: ceded losses divided by ceded premium.
• Ceded Losses: $6,300,000
• Ceded Premium: $12,000,000
• Reinsurer Loss Ratio: 52.500%

Combined Ratio Waterfall Chart

Builds a stacked bar chart showing the reinsurer combined ratio components: loss ratio, ceding commission, and expense ratio.
• Reinsurer Loss Ratio: 52.500%
• Ceding Commission Rate: 30.000%
• Reinsurer Expense Ratio: 12.000%
• Combined Ratio Waterfall Chart:
Loss RatioCeding CommissionExpense Ratio
Requested result for Combined Ratio Waterfall Chart included above.
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02 The comparison

Watch how LLMs really work.

One prompt. Ten runs each. Nothing staged.
The prompt, sent to each“A 7,000,000 deal: NOI 450,000 growing 3%, 5-year hold, 65% LTV at 7% on 30-year am, closing 1.5%, exit cap 6.5%, selling costs 2%. What's my levered IRR?”
The exact answer · 5-year levered IRR
10.8463781499708%
● RAW LLM
0/10 exact
methods10 distinct
avg time29.7 s
energy / call~1.5 Wh
● TRUEMATH
10/10 exact
method1, auditable
avg time3.1 s9.6× faster
energy / call~0.003 Wh~500× less
Claude Opus 4.8 vs TrueMath via natural language, 10 runs each. Energy is inference-only; datacenter cooling widens the gap.
TrueMath was 9.6x faster, 500x more energy efficient, and delivered 10 identically precise answers using one fixed auditable method.
That's the receipt.

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