Gains:
- Ability to establish the damage development triangle, IBNR (incurred but unreported damage) and chain-ladder method with the support of artificial intelligence and interpret the development factors
- Ability to compare results with alternative methods such as Bornhuetter-Ferguson and Mack and explain reserve uncertainty (variability, confidence interval) with artificial intelligence
- Being able to maintain that the provision figure calculated by artificial intelligence is a draft, not final, and that the choice of development factor and judicial correction belongs to the responsible actuary.
When an insurance company pays for a damage today, it actually pays off the debt of a policy it sold in the past. But not every damage is reported immediately and not every reported damage is paid in full immediately. A traffic accident occurs today, the company is notified three months later, the court process takes two years, and the final payment becomes clear after four years. Therefore, the company must reserve money today for damages that have not yet been fully paid or even not yet reported. This money is called the reserve, and its accurate calculation is an insurance company's most critical actuarial task. If he leaves less, the company will go into bankruptcy; If too much is allocated, the capital is tied up in vain and the profit is hidden.
In this unit, we will cover the three concepts at the heart of provision accounting: the damage development triangle, IBNR and the chain-ladder method. Then we will consider alternative methods (Bornhuetter-Ferguson, Mack) and uncertainty. The AI writes the code for these calculations, fills in the triangle, calculates the factors and explains the result; but the responsibility for the development factor selection, judicial correction and final provision figure lies with the responsible actuary.
What is the damage development triangle?
The basis of the provision calculation is the development triangle / run-off triangle. The rows show the period in which the damage occurred (accident year), and the columns show how much was paid for that damage (development year). It reads like this: 4 million was paid in the 1st development year of the 2021 accident year, a cumulative 6.2 million was paid in the 2nd year, and 7 million was paid in the 3rd year. The old accident years have matured (almost all payments have been made), while the new years are still developing. Hence the name of the triangle: the lower right corner is empty, because the further development of the new years has not yet occurred. The actuary's job is to estimate this empty corner.
IBNR (Incurred But Not Reported) is precisely part of this gap: the future cost of claims that have occurred but have not yet been reported to the company. There is also IBNER (additional development of reported but under-reserved claims). In practice, triangle methods estimate the total required provision (paid + future development); When you subtract the paid portion, the remaining provision remains, including IBNR.
Tip: You can set up the triangle on two different bases: "damage paid" and "damage incurred (paid + known reserve)". Examining the two together helps you capture the change in claims teams' booking behavior.
Chain-ladder step by step
The chain ladder is the most common response method, and its logic is intuitive: if losses in the past have grown at a certain rate on average from one development year to the next, new years will grow at a similar rate. Steps:
- Set up the cumulative triangle. Sort the cumulative paid claims for each accident year by year of development.
- Calculate development factors. For each column pass: sum of next column / sum of current column (using only rows with both columns occupied). For example, the factor 1→2 is 1.45; The factor 2→3 can be 1.12. This factor is called age-to-age factor.
- Find cumulative (stacked) factors. Multiplying the remaining factors to reach each year's final.
- Fill the empty corner. Estimate the ultimate damage by multiplying the last known value of each new accident year by the remaining factors.
- Calculate the response. Final damage − paid to date = provision payable in the future (including IBNR).
The following table is a mini example (cumulative paid damage, million TL):
accident year
Come on. 1
Come on. 2
Come on. 3
Come on. 4
2021
4.0
6.0
6.8
7.0
2022
4.4
6.5
7.3
?
2023
4.8
7.0
?
?
2024
5.2
?
?
?
In this triangle, the factor 1→2 is approximately 1.47; 2→3 about 1.12; 3→4 equals approximately 1.03. 2024 final 5.2 × 1.47 × 1.12 × 1.03 ≈ 8.82 million; Since the amount paid is 5.2, the provision is ≈ 3.62 million TL. The AI does this arithmetic in seconds, but the actuary decides whether the factors are reasonable.
Alternative methods and uncertainty
The chain ladder alone is not sufficient because development factors are extremely sensitive to small fluctuations because there is little data in recent accident years; A single major damage can blow away the entire estimate. That's why the Bornhuetter-Ferguson (BF) method is used: BF estimates the undeveloped part by using an external expected loss ratio information and thus smoothes volatility. Chain ladder is preferred in mature years, BF is preferred in new and immature years; Together they give a balanced estimate.
To measure uncertainty, the Mack method is used: it analytically gives the standard error (variability) of the chain ladder estimate. Additionally, a full probability distribution of the response can be produced by bootstrap (simulation by repeatedly sampling the data); This answers the question (critical to Solvency II) of “what would our response be in the worst case scenario?” AI is very powerful in generating code and comparison of these methods.
Caution: Growth factor selection is not mechanical. In one year, a change in legislation, a large wave of lawsuits, or a change in the rate of claim payment may disrupt the factors. The choice of "simple average, weighted average, last 3 years" is judicial and must be justified.
How to use AI in reserve accounting
1) Chain ladder code:
Write a commented code in Python that calculates the chain-ladder. Input: cumulative paid damage triangle (list of lists, missing cells None). 1) Calculate the volume-weighted age factor for each column pass. 2) Find the cumulative factors. 3) Fill in the blank corner and estimate the final damage for each accident year. 4) Calculate and sum the compensation (final - paid). Print each intermediate step to the screen; don't make up a library, use basic Python.
2) Method comparison:
Explain to an actuary the difference between a chain ladder and Bornhuetter-Ferguson.- Which is more reliable in which situation?- Why is BF preferred in new (immature) accident years?- How do I determine the 'expected damage rate' required for BF? Summarize the pros/cons in a table.
3) Factor plausibility check:
I have the following age-to-age factors: 1->2: 1.47; 2->3: 1.12; 3->4: 1.03; 4->5: 1,45.The 4->5 factor looks strange compared to the others.- What could be the possible reasons for this jump (regulatory, major damage, data error)?- What checks should I do to verify?Decision making; Give me a checklist.
4) Uncertainty interpretation:
My chain ladder best guess provision is 42 million TL, Mack standard error is 5.3 million. How do I explain this to a manager and a regulator?- Explain in plain language what the 75% and 99.5% levels mean.- How can I convey the message 'range instead of single number'?
Weak prompt / Strong prompt
Weak prompt:
Calculate my reward.
There is no triangle, no method, no data. AI fits the gap.
Powerful prompt:
Your role: booking assistant. I will give you the cumulative paid claims triangle (anonymous, million TL):2021: [4.0, 6.0, 6.8, 7.0]2022: [4.4, 6.5, 7.3]2023: [4.8, 7.0]2024: [5.2]Task:1) Calculate the weighted age-to-age factors, each show.2) Fill in the blank corner, write the final loss of each year.3) Calculate the total provision (final - paid).4) 2024 is very new; So explain why your estimate is more uncertain. Show me the intermediate numbers so I can verify them manually. Just use the data I give you.
three mini cases
Case 1 — Inadequate provision. One company calculated the last two accident years in its fast-growing traffic portfolio with a straight chain ladder. Since the new years' factors were low, the provision was estimated at 31 million TL. When the actuary checked with BF and used the expected damage rate, the realistic response was 44 million TL. The difference of 13 million was confirmed with real damages a year later. Lesson: in new years, the mere chain deceives the ladder.
Case 2 — Corrupted factor. An assistant actuary saw a 3→4 factor of 1.42 in the triangle that the AI produced; whereas the historical average was 1.05. If it had passed without questioning, the response would have inflated by approximately 30 percent. The investigation revealed that two accident years were shifted due to a data loading error. The AI didn't produce the error, but it didn't notice it; The actuary's reasonableness check caught on.
Case 3 — Correct presentation of uncertainty. A responsible actuary told management only that "the provision is 42 million." The management thought this was certain and distributed profits. The next year, when the real figure was 48 million, a crisis arose. Next term, the actuary offered a range with Mack and bootstrap saying "best guess is 42, but 75% level is 46, 99.5% level is 55 million"; The management made its decision accordingly. It saved a lot of time in preparing the AI bootstrap code and chart.
Common mistakes
- Using only the chain ladder in recent years of accidents. Less data means volatile factor; Balance with BF.
- Not subjecting development factors to reasonableness control. One corrupt factor blows away the entire response; Compare with historical pattern.
- Presenting the reciprocal as a single exact number. The response is a guess; Presenting it without an uncertainty range (Mack, bootstrap) is misleading.
- Confusing the paid and realized triangle. The two measure different things; Work consistently on one basis or consciously compare the two.
- Ignoring inflation and regulatory breaks. The past development pattern may not remain the same in the future; Also consider structural change.
In summary
The reserve is the present estimate of future liability and is the insurance company's most critical actuarial calculation. The past payment pattern is seen with the development triangle; The chain ladder fills the empty corner with age-by-age factors and estimates the final damage and compensation including IBNR. In new years, BF is more stable; Uncertainty is measured by Mack and bootstrap. The AI fills in the triangle, writes the code, and compares the methods; but the factor selection, reasonableness check and final figure depend on the judgment and signature of the responsible actuary.
Application task
Create an anonymous mini triangle of cumulative paid claims (4 accident years × up to 4 development years). Ask the AI to calculate the equivalent with the chain ladder. Manually verify the age-by-age factors and the final of 2 years. Then ask the AI “how would BF have produced a different result for the most recent year” and compare the two methods. Consciously distort one of the factors (for example, enlarge a cell by 10 times) and observe how the AI's response changes and how the plausibility check will catch this.
checklist
- [ ] Am I consistent in whether I set up the triangle based on damage paid or damage incurred?
- [ ] Have I checked the plausibility by comparing the age-age factors with the historical pattern?
- [ ] Have I cross-checked with BF for new/immature years?
- [ ] Did I present the response with an uncertainty range rather than a single number?
- [ ] Have I independently recalculated the final damage and counter arithmetic?
- [ ] Have I put the justification for my factor selection (average type, period) in writing?