Every answer and its explanation appears here once you have finished the path. Each one then links to the matching glossary entry, where the concept is set out in full with its worked example.
1. A motor book records 1,200 claims for 10,000 policy-years of exposure. What is its claim frequency?
0.12, that is 12 claims per 100 policy-years of exposure
Frequency relates a number of claims to the exposure that produced them: 1,200 divided by 10,000 policy-years gives 0.12. The raw claim count says nothing until one knows the exposure it was observed on. The inverse ratio, 8.3, is an average time between two claims, not a frequency. The share of policyholders affected is not the same thing either: a policyholder reporting two claims counts twice in the frequency and once among the policyholders with a claim. The figure is also sensitive to the claim definition used, with or without files that stayed below the deductible, and exposure must be counted the same way as the claims.
Glossary entry →2. On the same book, total losses are 3,600,000 EUR for 1,200 claims, and a single file costs 500,000 EUR. To price the attritional losses, the actuary caps that file at 150,000 EUR. Why?
So one extreme case does not skew the attritional average, the excess being priced separately
Severity is total losses divided by the number of claims, here 3,000 EUR. An average can be dragged by a single extreme value, and a 500,000 EUR file alone weighs more than a hundred ordinary claims. Capping does not make the cost disappear: the part above the threshold is taken out of the attritional losses and priced separately, as a large-loss load. Two phenomena that do not follow the same laws are thus kept apart. It is also why the whole distribution is monitored and not just the mean: a stable average severity can hide a tail that is getting heavier.
Glossary entry →3. On 2,000 SME cyber policies, an actuary observes 40 claims in the year, at an average cost of 80,000 EUR. What is the pure premium per policy?
1,600 EUR
The pure premium is the expected claims cost per policy: frequency times severity. Frequency is 40 out of 2,000, or 2%, and 2% of 80,000 EUR gives 1,600 EUR. The figure of 2,480 EUR is the commercial premium reached after 55% loadings for expenses, cost of capital and margin: it is no longer the pure premium. 3,200,000 EUR is the cost of the whole book, not of one policy, and 40 EUR divides the average claim cost by the number of policies, which measures nothing. In cyber, this simple calculation is the most fragile in the trade: the threat moves fast, the history is short, and policyholders' claims are not independent.
Glossary entry →4. A motor insurer grows from 1,000 to 100,000 insured drivers, independent and similar. What does the law of large numbers give it?
A more predictable average cost per policy, though each driver's claim stays uncertain
The law of large numbers says that the observed average of many realizations of the same random event converges toward its expectation. It changes neither each driver's risk nor the expectation itself: the pure premium per policy stays the same; what narrows, in proportion, is the gap between observed and expected losses. This is what allows a stable premium and risk pooling. Its condition, often left unsaid, is independence: if all the drivers depended on the same faulty driving software, predictability would collapse, whatever the size of the book.
Glossary entry →5. True or false: risk pooling works however policyholders' losses occur, provided there are enough policyholders.
False
False. The premiums of the many pay the losses of the few because not everyone suffers a loss at the same time. Numbers are not enough: risks must also be relatively independent. A war, a pandemic or a systemic cyberattack strikes many policyholders at once, and no book size absorbs a loss that hits everyone together. Such risks call for other mechanisms: reinsurance, transfer to capital markets, public support.
Glossary entry →6. At year-end, an insurer books 50 million euros for reported, unsettled claims, and 18 million for claims incurred but not yet reported. What do these 68 million represent?
Its claims reserves: the estimated future cost of claims that have already occurred
Claims reserves are a liability: the cost still to be paid on claims that had already occurred at the reporting date. They combine reported files, estimated one by one, and claims incurred but not yet reported, the IBNR, estimated by statistical methods. They do not cover future claims, which belong to next year's premium, and they are not a profit: they are the heaviest and most uncertain item on a non-life insurer's balance sheet. Under-reserving flatters one year and defers the loss; a pickup in judicial inflation, for example, forces these amounts to be strengthened the following year.
Glossary entry →7. An annual contract taken out on April 1 covers agricultural hail for the April to September season only. On December 31, the season is over and the premium has been collected in full. What unearned premium reserve should be carried at that date?
None: premium follows the risk, and the risk is over
The unearned premium reserve isolates the part of premium that relates to cover still to run: it is a debt to the policyholder, not income. Pro rata temporis only holds if risk is spread evenly over the year. Hail cover is earned with the season, and after September there is no risk left to cover: the correct reserve is nil, whereas the calendar would leave one. Hail claims still to be settled do not belong in this reserve but in claims reserves. And when unearned premium is not enough to pay the claims of the remaining period, an unexpired risk reserve takes over.
Glossary entry →8. A cyber insurer covers several thousand SMEs across different sectors and countries. It finds that 40% of them depend on the same cloud email provider. Why is its book less diversified than it looks?
A single outage there can hit them all at once: their risks are no longer independent
Accumulation, or aggregation, is a concentration of exposures that one event can hit together. In natural catastrophe it is geographic, so visible on a map: a hurricane strikes an area. In cyber it is logical: it follows shared digital dependencies, ignores distance and does not show in the list of sectors and countries. Apparent diversification therefore protects against nothing if one outage reaches 40% of the book. Aggregation is managed through mapping common providers, scenarios, sublimits, exclusions and reinsurance, with a difficulty peculiar to cyber: data too young to calibrate those scenarios with confidence.
Glossary entry →9. In July 2024, a faulty update pushed by a security software vendor simultaneously grounds airlines, hospitals and banks. What does the event illustrate for a cyber insurer?
A single point of failure: a shared component whose outage hits separate sectors at once
The global outage caused in July 2024 by a CrowdStrike update was not an attack: no war clause had any role to play, and the event was all the more instructive for it. A single security vendor, present in transport, healthcare and finance companies, was enough to stop them all on the same day. That is the definition of a single point of failure: a shared component whose failure spreads to everyone who depends on it. Diversifying by sector gives no protection against a common dependency, and such dependencies are often invisible at underwriting, a policyholder frequently not knowing which providers support its own suppliers.
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