Gains:
- Being able to establish and interpret the distinction between damage frequency and damage amount (severity), appropriate distributions (Poisson, negative binomial, gamma) and composite model logic with the support of artificial intelligence.
- Sorting out extremely large losses (outliers/large losses), data capping and trend/development corrections to artificial intelligence with the right questions and data.
- Ability to understand that the distribution selection and parameters produced by artificial intelligence should be confirmed by goodness-of-fit tests and actuarial reasoning.
The most basic question for an insurance company is: "How much damage will we pay for this policy group next year?" Answering this question correctly is a prerequisite for both setting the premium correctly and allocating sufficient reserves. Actuaries answer this question by dividing it into two; because it is much more accurate to model two separate behaviors separately instead of estimating the total damage in one piece. These two parts are frequency and intensity.
Frequency (frequency of damage) is how many damages occur per given exposure; For example, 100 vehicles - 8 accidents per year. Severity is the average amount of each damage incurred; for example, 30,000 TL per accident. Multiplying the two gives the risk premium: expected damage cost per exposure (0.08 × 30,000 = $2,400). In this unit we will see step by step how to use AI to establish this distinction, choose the right probability distribution, and manage outliers. Let's remind from the beginning: AI proposes distributions and writes code, but it is up to the actuary to confirm the choice of distribution through goodness-of-fit tests and judgment.
Why are frequency and intensity modeled separately?
Frequency and intensity show different statistical behavior. The number of claims is a count variable (0, 1, 2, 3...) and is usually modeled with a Poisson distribution or a negative binomial distribution if there is overdispersion (variance > mean). Poisson is the classical distribution that models the number of rare and independent events. Damage amount is a continuous and right-skewed variable: most claims are small, a few claims are very large. Therefore, severity is often modeled with a gamma or lognormal distribution; these are positive and right-skewed distributions.
Modeling the two separately has three concrete benefits. First, you can see that each has its own drivers (risk factors): young driver increases frequency, expensive vehicle increases violence. Second, when the data changes, you can diagnose why: has the damage cost or the number of claims increased? Third, you can only consider extreme large losses separately on the violence side. The combination of these two is called a compound model; expected total damage = expected frequency × expected severity.
Hint: The sentence "Our loss/premium ratio has increased" does not say anything on its own. Separate the question of whether frequency or intensity increased; intervention (price, coverage, damage management) would be completely different.
Outliers, truncation and trend corrections
Damage data in its raw form is not ready for model building. Three corrections are almost always required. The first is extreme/major damage sorting: a few giant damages (e.g. a factory fire) skew the average; these are modeled as a separate "major damage load". The second is capping: fixing very large damages to a certain ceiling (for example 1,000,000 TL) and calculating the upper part separately makes the model stable. Third, trend and development correction: past claims should be updated with inflation to today's price level (trend), and claims that have not yet been fully paid should be brought to their final level (development — we will cover this topic in unit 3).
The following table compares the properties of the two components:
feature
Frequency (frequency)
Violence (amount)
Variable type
Counting (0,1,2...)
constant, positive
Typical distribution
Poisson, negative binomial
Gamma, lognormal
Master driver examples
Age, experience, region, use
Vehicle value, coverage limit, repair cost
Outlier problem
low
High (major damages)
Inflation effect
weak
strong
How to use AI in damage modeling
Where AI is strongest is in discussing the distribution choice, writing the code, and interpreting the result. Below are four copyable templates.
1) Discuss distribution selection:
Your role: actuarial modeling assistant. I have insurance claim AMOUNT data (anonymous, 1,600 claims). Summary: mean 30,300 TL, median 12,500 TL, maximum 940,000 TL, skewness is high. Question: would gamma or lognormal be more suitable for the severity model? What is the assumption of each, plus/minus and with which goodness-of-fit test (e.g. Explain that I will make a decision (Q-Q chart, K-S test, AIC).Making a definitive decision; Give me a comparison frame.
2) Frequency-intensity calculation code:
Write a commented code with Python + pandas that does the following steps: 1) There are 'exposure', 'claim_count', 'claim_amount' columns in the df. 2) General frequency = total claim_count / total exposure. 3) Average severity = total claim_amount / total claim_count. 4) Risk premium = frequency × severity. 5) Print each intermediate result to the screen so that I can verify it manually. Library fitting; just use pandas.
3) Extreme value / cutoff analysis:
I have an anonymous claim amount distribution. Claims such as 950,000, 720,000, 610,000 TL constitute 22% of the total amount. Tell me about your capping approach: - Which cap options are reasonable (e.g. 500K, 750K, 1M)? - How do I add back the cut portion as a separate "major damage load"? - Show me step by step how this decision affects the risk premium.
4) Translating the result into business language:
My frequency increased from 0.13 to 0.15; The average violence increased from 28,000 to 34,000 TL. Summarize this in 4 sentences that a manager can understand: - What happened, which component increased by how much? - What is the total effect on the risk premium? - Write the possible reasons and 2 assumptions that I need to verify.
Weak prompt / Strong prompt
Weak prompt:
Set up my loss model and calculate the premium.
Unclear: which data, which component, which distribution, which period? AI fills this gap with fabrication.
Powerful prompt:
Your role: actuarial modeling assistant. Data (anonymous, traffic branch, 2024): exposure 20,000 policy-years, number of claims 2,600, total damage 91,000,000 TL, the 5 largest damages total 12,000,000 TL. Task: 1) Calculate the frequency and raw average severity, show the formula. 2) The 5 largest damages Cap it to 1,000,000 TL and calculate the adjusted severity again. 3) Compare the risk premium with and without cap, comment on the difference. 4) Write each step with intermediate numbers so that I can verify it manually. Just use the numbers I gave; If it's missing, ask.
three mini cases
Case 1 — The power of separation. One actuary saw the loss/premium ratio in the housing branch rise from 68 percent to 81 percent in one year. Before the panic price increase was suggested, a frequency-severity distinction was made: the frequency was almost constant (0.041 → 0.043), but the average severity had jumped from 14,200 TL to 19,800 TL. The reason was construction cost inflation, not the number of policies or risky customers. The correct intervention was to update the coverage amounts, not a blind premium increase.
Case 2 — Outlier trap. The average of 1,800 claims in a business insurance portfolio was 42,000 TL. However, a single fire damage of 6.4 million TL alone inflated this average by approximately 3,500 TL. When this major damage was modeled and capped as a separate "major damage burden", the base severity decreased to 38,500 TL and the premium became more fair. AI quickly generated capping code and alternative caps; The actuary made the decision.
Case 3 — Maldistribution. Without question, an assistant ran an AI code that selected a normal (Gaussian) distribution for severity. Because the normal distribution allowed for negative values and symmetry, it did not fit right-skewed damage data; the model overestimated small damages and underestimated large ones. When the Q-Q plot and AIC were compared, it was seen that gamma fit much better. Lesson: The distribution proposed by the AI is always tested by fit testing.
Common mistakes
- Combining frequency and intensity and predicting with a single model. It hides two different behaviors; you lose the driver and why.
- Averaging without eliminating extreme/major damage. A few giant damages distort the whole picture; premium is artificially inflated.
- Using old damage without applying inflation trend. The 2019 damage is not the same as today's price; trend correction is necessary.
- Fitting a normal distribution to right-skewed data. The assumption of negative value and symmetry is contrary to damage data; Think gamma/lognormal.
- Not verifying the distribution choice with fit testing. AI's proposal is a start; Confirm with Q-Q, K-S, AIC.
Attention: Cap (cutting) level is not chosen arbitrarily. Too low a ceiling hides the risk of major damage; too high a ceiling makes trim useless. Choose by looking at the portfolio's past major loss experience and reinsurance terms.
In summary
The way to accurately estimate total damage is to divide it into frequency (frequency) and severity (amount). Frequency is modeled by Poisson/negative binomial, intensity by gamma/lognormal; The risk premium is found by multiplying the two. Raw data requires outlier removal, truncation, and trend correction. AI distribution discussion is an excellent assistant for code and commenting; but the distribution selection and cap decision are confirmed by fit tests and actuarial judgment.
Application task
Prepare an anonymous damage summary (exposure, number of claims, total damage, top 3-5 claims). Ask the AI to calculate (a) the raw frequency-severity-risk premium, (b) cap large losses and calculate the adjusted risk premium. Verify the two results by hand and note by what percentage capping changes the risk premium. Then ask the AI the question "gamma or lognormal for violence" and summarize the comparison frame it gives in your own words.
checklist
- [ ] Did I calculate frequency and intensity separately, or did I look at them as one piece?
- [ ] Have I identified major/extreme damage and dealt with it separately?
- [ ] Have I applied inflation/trend adjustment to old claims?
- [ ] Have I verified the intensity distribution with a goodness-of-fit test?
- [ ] Have I independently recalculated the risk premium (frequency × severity)?
- [ ] Did I question the distribution and cap level suggested by the AI and confirm it with judgment?