Institute and Faculty of Actuaries (IFoA) Exams General Insurance Specialism (SP7, SP8, SA3) Syllabus

General Insurance Specialism (SP7, SP8, SA3) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for General Insurance Specialism (SP7, SP8, SA3) in Institute and Faculty of Actuaries (IFoA) Exams, not a summary of it.

1. 1

   General Insurance Products and the Market

   3 topics

   • Lines of business
     • Personal lines: motor, household, travel
     • Commercial lines: liability, property, marine, aviation
     • London Market and reinsurance business
   • Policy structures and coverage
     • Claims-made vs losses-occurring policies
     • Excesses, deductibles and limits
   • Reinsurance products
     • Proportional: quota share and surplus
     • Non-proportional: excess of loss and stop loss
2. 2

   Reserving (SP7)

   3 topics

   • Deterministic reserving methods
     • Chain ladder and development factor methods
     • Bornhuetter-Ferguson method
     • Average cost per claim methods
   • Stochastic reserving
     • Mack model and bootstrap techniques
     • Estimating reserve uncertainty and ranges
   • Reserving considerations
     • IBNR and IBNER allowances
     • Discounting and inflation in reserves
     • Reinsurance recoveries and bad debt
3. 3

   Pricing (SP8)

   3 topics

   • Rating methodologies
     • Burning cost and frequency-severity approaches
     • GLM-based rating and rating factors
     • Credibility and experience rating
   • Data and assumptions
     • Exposure measures and claims data adjustments
     • Trends, large losses and catastrophe loading
   • Pricing the reinsurance and the price
     • Office premium build-up and loadings
     • Pricing non-proportional reinsurance
4. 4

   Capital and UK Regulation (SA3)

   3 topics

   • Capital modelling
     • Internal capital models and risk aggregation
     • Catastrophe modelling and accumulation control
   • Solvency II for general insurers
     • Premium and reserve risk in the standard formula
     • Lloyd's capital setting and oversight
   • Financial reporting and management information

General Insurance Specialism (SP7, SP8, SA3) flashcards for Institute and Faculty of Actuaries (IFoA) Exams

24 of 63 cards from the General Insurance Specialism (SP7, SP8, SA3) deck — real questions with worked answers.

1. In general insurance, what is meant by a "line of business" (class of business)?

   A grouping of policies that cover similar types of risk and share broadly homogeneous claim characteristics (e.g. motor, property, liability, marine). Lines are used for pricing, reserving and reporting so that experience can be analysed on like-with-like exposures.

2. Distinguish "short-tailed" from "long-tailed" lines of business, giving an example of each.

   Short-tailed: claims are reported and settled quickly after the event (e.g. property/household). Long-tailed: a long delay between the event and final settlement (e.g. employers'/public liability, motor bodily injury). Long-tailed lines carry greater reserving uncertainty and investment/inflation risk.

3. What is the difference between a "claims-occurring" (losses-occurring) and a "claims-made" policy basis?

   Claims-occurring covers claims arising from events that occur during the policy period, whenever reported. Claims-made covers claims first reported (made) during the policy period, regardless of when the event occurred. Claims-made is used for very long-tailed liability lines to limit the insurer's IBNR tail.

4. Define the following policy terms: excess (deductible), limit, and coinsurance (proportional retention).

   Excess/deductible: amount of each claim borne by the policyholder before the insurer pays. Limit: maximum the insurer will pay per claim or in aggregate. Coinsurance: the policyholder retains a fixed proportion of each loss (insurer pays e.g. 80%), sharing losses above the deductible.

5. Explain the difference between an each-and-every-loss (EEL) deductible and an aggregate deductible.

   An EEL deductible applies separately to every individual claim. An aggregate deductible applies to the total of all claims over the policy period; the insurer only pays once cumulative retained losses exceed the aggregate amount.

6. What is the purpose of a policy aggregate limit, and how does it differ from a per-occurrence limit?

   A per-occurrence limit caps the insurer's payment for any single occurrence/claim. An aggregate limit caps the total paid across all claims in the policy period. The aggregate protects the insurer against frequency accumulation; per-occurrence protects against severity of a single event.

7. What are the two broad categories of reinsurance, and how do they differ in how risk is ceded?

   Proportional: cedant and reinsurer share premiums and losses in a fixed proportion (quota share, surplus). Non-proportional: reinsurer pays only the part of losses above a retention/excess point (excess of loss, stop loss); premium is not a fixed share of the original.

8. Contrast quota share and surplus reinsurance.

   Quota share: a fixed proportion $\alpha$ of every risk is ceded (same percentage for all policies). Surplus: the cedant retains a fixed monetary line and cedes the surplus above it, so the ceded proportion varies by risk size, allowing the cedant to keep more of small risks.

9. Describe the three main types of non-proportional (excess of loss) reinsurance.

   Risk XL: applies to each individual risk/loss. Catastrophe (cat) XL: applies to the accumulation of losses from a single catastrophic event across many policies. Aggregate (stop loss) XL: applies to the cedant's total losses over a period, protecting the loss ratio.

10. What is a reinstatement in an excess-of-loss reinsurance treaty?

    A reinstatement restores the cover limit after it has been eroded by a claim, allowing the layer to respond to further losses. Treaties specify the number of reinstatements and whether they are free or paid (reinstatement premium charged, often pro-rata to amount and/or time).

11. Distinguish facultative reinsurance from treaty reinsurance.

    Facultative: individual risks are reinsured one at a time, each separately underwritten and accepted/declined. Treaty: an agreement covering a whole portfolio/class automatically, with all qualifying risks ceded under agreed terms without case-by-case acceptance.

12. What is the run-off triangle (development triangle) and what does each axis represent?

    A triangle of cumulative (or incremental) claim amounts arranged by origin period (e.g. accident/underwriting year) down the rows and development period (delay since origin) across the columns. The lower-right is unobserved and is projected to estimate ultimate claims and reserves.

13. Describe the basic chain ladder method for estimating ultimate claims.

    Estimate development factors $f_j = \dfrac{\sum_i C_{i,j+1}}{\sum_i C_{i,j}}$ from cumulative claims, then project each origin year forward: $\hat{C}_{i,n} = C_{i,j}\prod_{k\ge j} f_k$. The reserve is ultimate minus paid/incurred to date. It assumes future development mirrors the past and is stable across origin years.

14. State the key assumptions underlying the basic chain ladder method.

    (1) Development factors are the same for all origin years (stable development pattern). (2) Future inflation/claims development follows the historic pattern. (3) The first origin year is fully run off (or a tail factor is applied). (4) No distortions from changes in mix, claims handling, or one-off events.

15. Describe the Bornhuetter-Ferguson (BF) method and how it differs from the chain ladder.

    BF blends an a-priori expected ultimate (e.g. premium $\times$ expected loss ratio) with the chain ladder development pattern: reserve $= U^{prior}\times(1 - \frac{1}{f})$ where $\frac{1}{f}$ is the proportion developed. Unlike the chain ladder it does not over-rely on sparse early data, so it is more stable for immature/recent origin years.

16. Write the Bornhuetter-Ferguson reserve formula and define the terms.

    $$R_i = U_i^{prior}\left(1 - \frac{1}{f_i}\right)$$ where $R_i$ is the reserve for origin year $i$, $U_i^{prior}$ is the a-priori ultimate (often premium $\times$ ELR), and $\frac{1}{f_i}$ is the cumulative proportion of claims expected to be developed/reported to date (the reciprocal of the remaining development factor product).

17. What is the average cost per claim (ACPC) reserving method?

    It projects claim numbers and average claim amounts separately: estimate ultimate claim counts (e.g. via a frequency triangle) and ultimate average cost per claim, then ultimate cost $=$ ultimate number $\times$ ultimate average. Useful when frequency and severity behave differently and require explicit inflation adjustment.

18. Why might an actuary adjust paid-claims data for inflation before applying a deterministic reserving method (the inflation-adjusted / Berquist-Sherman approach)?

    Because past claim payments reflect historic claims inflation; if future inflation differs, raw development factors mis-state the tail. Adjusting payments to a common price level removes past inflation, the projection is done in real terms, then explicit future inflation is reapplied so the assumption is transparent and controllable.

19. What is the Mack model, and what does it add to the chain ladder?

    The Mack model is a distribution-free stochastic model that reproduces chain ladder estimates while providing a formula for the mean square error of prediction (standard error) of the reserves. It estimates variability without assuming a full distribution, only specifying the first two moments of the development process.

20. Describe the over-dispersed Poisson (ODP) model used in stochastic reserving.

    Incremental claims are modelled as $C_{ij}\sim$ over-dispersed Poisson with mean $m_{ij}=x_i y_j$ (row $\times$ column parameters) and variance $\phi m_{ij}$, where $\phi$ is the dispersion parameter. Its maximum-likelihood point estimates reproduce the chain ladder, and it can be bootstrapped to obtain a full predictive distribution of reserves.

21. What is bootstrapping in the context of stochastic reserving and what does it produce?

    A simulation technique that resamples (with replacement) the residuals of a fitted reserving model to generate many pseudo-datasets, refitting each to build an empirical predictive distribution of the reserves. It produces estimates of reserve variability and percentiles (e.g. for risk margins / capital) without strong distributional assumptions.

22. Distinguish the standard error of prediction from the standard error of estimation in reserving.

    Estimation error (parameter error) reflects uncertainty in the fitted parameters. Prediction error additionally includes process error (random variation of future claims about their mean). Mean square error of prediction $=$ process variance $+$ estimation variance, so prediction error $\geq$ estimation error.

23. What is a "risk margin" in reserving and why is it held?

    An amount added to the best-estimate (mean) reserve to allow for uncertainty, so the total provision is more likely to be sufficient. Under Solvency II it is calculated using a cost-of-capital approach reflecting the cost of holding capital to support the run-off of the liabilities until settlement.

24. List several factors an actuary should consider that may distort a run-off triangle.

    Changes in: claims-handling/reserving philosophy, mix of business, policy terms (limits, excesses), rate of settlement (speed-up/slow-down), inflation, large/catastrophe losses, court/legislative changes, and reinsurance arrangements. Each can break the assumption that past development predicts future development.

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