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IAI SP7 practice questions

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Question 1Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In the standard volume-weighted chain ladder method, how is the development factor from one development period to the next calculated?

  1. The ratio of summed cumulative claims in the later period to the summed earlier period Correct answer.
  2. The arithmetic mean of the individual year-on-year cumulative claim ratios in the triangle
  3. The ratio of the latest diagonal cumulative claims to the earliest diagonal cumulative claims
  4. The median of the individual year-on-year cumulative claim ratios in the triangle

Explanation

The volume-weighted chain ladder factor is the sum of cumulative claims in the later development column divided by the sum in the earlier column, so larger origin years carry more weight in the estimate. This is the standard deterministic chain ladder estimator, while simple averages or medians are alternative estimators rather than the volume-weighted factor.

Question 2Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

Which liability component in general insurance technical provisions represents claims that have occurred but have not yet been reported to the insurer?

  1. The provision for claims incurred but not yet reported to the insurer Correct answer.
  2. The reserve for unexpired risks on policies still in force
  3. The allowance for claims handling expenses on known reported claims
  4. Case reserves set by claims handlers for reported claims

Explanation

IBNR is the liability for claims that have occurred before the valuation date but had not been reported by that date. It sits alongside case reserves for known claims and may include an allowance for claims handling expenses where the reporting regime requires it.

Question 3Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

An unexpired risk reserve is recognised when which condition is met?

  1. Reinsurance recoveries are expected to be delayed beyond the reporting date
  2. Investment income is lower than the discount rate used in the reserves
  3. Expected future claims and expenses exceed the unearned premium reserve Correct answer.
  4. Reported claims exceed the case reserves held by claims handlers for those claims

Explanation

An unexpired risk reserve, also called a premium deficiency reserve, is held when the unearned premium is insufficient to cover expected future claims, expenses and any required margin on the remaining cover. It is a liability for the unexpired period rather than a response to reporting delays or reinsurer weakness.

Question 4Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

For a very immature origin year, which input dominates the Bornhuetter-Ferguson ultimate estimate?

  1. The chain ladder ultimate, because it uses all observed development in the triangle
  2. The tail factor, because it extends the development pattern beyond the observed data
  3. The prior expected loss ratio applied to earned premium Correct answer.
  4. The observed paid claims to date, because they reflect the latest available experience

Explanation

In the Bornhuetter-Ferguson method the ultimate is the sum of paid claims to date and an expected unreported portion based on a prior loss ratio applied to earned premium. For an immature origin year the unreported portion is large, so the prior expected loss ratio dominates; as the year matures the estimate moves toward the chain ladder result.

Question 5Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

When general insurance technical provisions are discounted, which discount rate is most appropriate?

  1. No discounting at all, because general insurance claims are always short-tailed
  2. The insurer's expected return on equity, as a proxy for investment return
  3. A higher discount rate, which would increase the technical provision
  4. A rate reflecting the timing and currency of the claim payments Correct answer.

Explanation

Discounting converts expected future claim payments to a present value using a rate consistent with the timing and risk of those liabilities. A higher discount rate lowers the present value of the provision, and the insurer's return on equity is not an appropriate liability discount rate.

Question 6Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In Mack's stochastic chain ladder model, what gives rise to parameter estimation error in the reserve estimate?

  1. Cumulative claims are assumed to follow a normal distribution
  2. The development factors are estimated from a finite triangle Correct answer.
  3. Individual claim payments are random around their expected value, creating process variance
  4. The tail factor is always set equal to one

Explanation

Mack's model decomposes the mean squared error into process variance, which reflects random variation in claim outcomes, and parameter estimation error, which arises because development factors are estimated from a finite triangle. The latter reflects uncertainty about the true development pattern rather than the randomness of individual payments.

Question 7Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

The average cost per claim method is most appropriate for estimating ultimate claims when which condition holds?

  1. The insurer writes only very large single claims
  2. Claim counts are reliable and average claim cost is stable Correct answer.
  3. The number of reported claims is stable and average claim cost is highly volatile
  4. There are no reported claims in the most recent origin years

Explanation

The average cost per claim method projects ultimate claims from estimated claim counts and an estimated average cost per claim. It is useful when counts are reliably reported and average cost is stable enough to estimate; if counts are missing or average cost is highly volatile, the method is unreliable.

Question 8Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

How should expected reinsurance recoveries be treated when presenting gross technical provisions?

  1. Recognised as a separate asset, subject to the reinsurer's creditworthiness Correct answer.
  2. Included in the unexpired risk reserve because they relate to future cover
  3. Ignored, because reinsurance is treated as off-balance-sheet in all reserving regimes
  4. Deducted from the gross reserve to produce the net reserve, with no separate asset

Explanation

Gross technical provisions are stated before reinsurance, and expected reinsurance recoveries are recognised as a separate asset rather than netted against the liability. The recoverable amount must be assessed for collectability, including the reinsurer's credit risk.

Question 9Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

A reserving actuary extends the chain ladder development pattern with a tail factor greater than one. What is the effect on the estimated ultimate for the latest origin year?

  1. It increases the estimated ultimate and therefore the IBNR Correct answer.
  2. It decreases the estimated ultimate because more development is assumed after the triangle
  3. It has no effect on the latest origin year because that year is already fully developed
  4. It reduces the unexpired risk reserve held for future cover

Explanation

A tail factor extends the development pattern beyond the latest observed development period; a factor greater than one increases projected ultimate losses and therefore the IBNR for origin years that are not fully developed. The effect is largest for the most recent origin years, which have the most development still to emerge.

Question 10Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

An insurer's historical claims triangle is in nominal amounts, and the chain ladder factors were estimated when claims inflation averaged 3% per year. If claims inflation is now expected to be 6% per year, what is the most appropriate reserving response?

  1. Adjust the development pattern or projected payments for the higher expected claims inflation Correct answer.
  2. Discount the reserves at a higher rate to offset the effect of higher claims inflation
  3. Apply the historic chain ladder factors unchanged, because they already embed all future inflation
  4. Reduce the tail factor to compensate for the higher expected claims inflation

Explanation

Historic chain ladder factors estimated in nominal terms reflect the claims inflation experienced in the historical period. If future claims inflation is expected to be higher, projected payments should be adjusted or the development pattern re-estimated on an inflation-adjusted basis; changing the discount rate does not correct the mismatch in nominal cash flows.

Question 11Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In a general insurance claims development triangle, what does an origin period represent?

  1. the period in which the claim was first notified to the insurer by the policyholder
  2. the period in which the reinsurance treaty was renewed for the insurer
  3. the period in which the claim was finally paid and closed by the claims team
  4. the period in which the insured event giving rise to the claim occurred Correct answer.

Explanation

An origin period groups claims by the period of occurrence, typically accident year or underwriting year depending on the reserving basis. Development age is measured from the end of that origin period, so notification and settlement dates fall into later development periods.

Question 12Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

At development age 12 months a cumulative paid claims triangle shows 1,200 for an origin year, and at age 24 months it shows 1,800. What is the 12-to-24 month age-to-age development factor?

  1. 1.200
  2. 0.667
  3. 600
  4. 1.500 Correct answer.

Explanation

The age-to-age factor is the later cumulative amount divided by the earlier cumulative amount: 1,800 divided by 1,200 equals 1.500. It is not the incremental amount of 600, and 0.667 is the inverse ratio.

Question 13Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

A new general insurance line has no usable claims development triangle and no credible claims history. The actuary has only an industry benchmark loss ratio and earned premium. Which method should be used to set the initial ultimate claims estimate?

  1. case outstanding development method
  2. average cost per claim method
  3. expected loss ratio method Correct answer.
  4. paid chain ladder method

Explanation

With no credible claims triangle, the expected loss ratio method applies a benchmark loss ratio to earned premium to estimate ultimate claims. Chain ladder, case development and average cost methods all require usable claims, case or count data.

Question 14Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In the case outstanding development method, how is the ultimate claims estimate derived?

  1. multiplying earned premium by a selected expected loss ratio for each origin year
  2. dividing reported claim counts by an assumed average cost per reported claim
  3. projecting case outstanding to ultimate with case factors and adding paid claims Correct answer.
  4. applying paid age-to-age factors to cumulative paid claims and then adding a tail

Explanation

The method projects current case reserves to their ultimate level using case outstanding development factors, then adds cumulative paid claims. The resulting ultimate case reserve less current case reserve gives the IBNR estimate.

Question 15Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

Which data condition most strongly supports using a frequency-severity reserving method instead of an aggregate chain ladder?

  1. large individual claims causing severe volatility in aggregate paid amounts
  2. frequent changes in case reserving philosophy between valuations
  3. no exposure data available for the origin periods
  4. stable claim counts and a credible severity pattern by origin period Correct answer.

Explanation

Frequency-severity separates claim count development from average cost development, so it works best when counts are stable and severity can be estimated credibly. Aggregate chain ladder is simpler when the combined paid or incurred pattern is stable.

Question 16Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

An insurer increases its case reserves for recent origin years, but actual claim payments are unchanged. In a paid chain ladder reserving exercise, what is the direct effect of this change on projected ultimate claims, all else equal?

  1. ultimate claims double to reflect the stronger case reserves held by the claims team
  2. ultimate claims decrease because fewer claims remain open and unpaid at the valuation date
  3. there is no direct effect because the paid claims triangle is unchanged Correct answer.
  4. ultimate claims increase in direct proportion to the increase in case reserves

Explanation

The paid chain ladder uses cumulative paid amounts and their development factors, so a change in case reserves does not enter the calculation. It would affect an incurred or case outstanding method, but not the paid triangle unless payment behaviour later changes.

Question 17Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

For a fixed undiscounted claims reserve and a fixed discount rate, which expected payment pattern produces the highest discounted reserve?

  1. payments timed to match the discount rate exactly
  2. payments delayed as far as possible into later years
  3. payments spread evenly over the settlement period
  4. payments made earlier in the settlement period Correct answer.

Explanation

Discounting reduces later payments more heavily, so bringing cash flows forward increases present value and therefore the discounted reserve. Delaying payments or spreading them evenly lowers the discounted amount relative to earlier payment.

Question 18Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

When setting technical provisions, how should an allowance for reinsurer default risk on expected reinsurance recoveries be reflected?

  1. reduce the expected recoverable by an allowance for expected credit losses Correct answer.
  2. include it only in the risk margin and never in the recoverable
  3. ignore it because reinsurance contracts are legally binding
  4. add it to the gross reserve as an unexpired risk reserve

Explanation

Reinsurance recoveries are an asset that may not be fully collectible, so the expected recoverable should be reduced for credit risk. This is separate from presenting gross technical provisions and from the unexpired risk reserve.

Question 19Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

Mack's distribution-free chain ladder model captures process variance and parameter estimation error. Which source of uncertainty lies outside its prediction error?

  1. model specification error from an incorrect development pattern Correct answer.
  2. correlation arising from the same data being used for several origin years
  3. random variation in future claim payments around the expected value
  4. uncertainty in the estimated chain ladder factors

Explanation

Mack's mean squared error of prediction includes process variance and estimation error conditional on the chain ladder model being correct. It does not allow for model error, such as the selected development pattern or tail being wrong.

Question 20Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In the Cape Cod, or Stanard-Bühlmann, method, how is the initial expected loss ratio estimated?

  1. from the latest diagonal of paid losses divided by the current case reserves
  2. from the selected tail factor applied to the most mature origin year
  3. solely from an external industry benchmark selected by the actuary
  4. from aggregate reported claims divided by exposure adjusted for the reported proportion Correct answer.

Explanation

Cape Cod estimates the expected loss ratio from the data by comparing reported claims with used-up exposure, where exposure is adjusted by the proportion of claims expected to be reported. That data-derived ratio is then used in a Bornhuetter-Ferguson-style calculation.

Question 21Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

When estimating the ultimate cost of claims for general insurance technical provisions, how should claims handling expenses that will be incurred in settling reported and unreported claims be treated?

  1. Recognised only after claim reporting.
  2. Offset against reinsurance recoveries.
  3. Excluded as operating expenses.
  4. Included within the claims provision. Correct answer.

Explanation

Claims handling expenses that will be incurred in settling both reported and unreported claims form part of the claims provision. They are not treated as general operating expenses to be excluded from technical provisions. The actuary should allow for them explicitly or through appropriate loadings.

Question 22Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In a cumulative claims development triangle, what does a diagonal running from bottom left to top right typically represent?

  1. The sum of all ultimate claims.
  2. The tail factor selected for the latest origin year.
  3. Development periods for one origin year.
  4. A single calendar or experience period. Correct answer.

Explanation

In a standard origin-period by development-period triangle, each bottom-left to top-right diagonal contains cells with the same calendar experience period. It links different origin years at different development ages.

Question 23Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

Under a cost-of-capital approach, the risk margin for general insurance technical provisions is intended to represent what?

  1. The margin for reinsurer default on recoveries.
  2. The cost of holding regulatory capital for reserve risk. Correct answer.
  3. The expected investment return on reserve assets.
  4. The allowance for claims inflation in the tail.

Explanation

The risk margin under a cost-of-capital approach remunerates the capital that would be held to support the non-hedgeable reserve risks. It is calculated by applying a cost-of-capital rate to projected required capital over the run-off.

Question 24Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

For an origin year that is moderately developed, how does the Bornhuetter-Ferguson ultimate estimate compare with the chain ladder ultimate when reported claims are below the expected level?

  1. BF is higher, as expected claims remain for the undeveloped part. Correct answer.
  2. BF cannot be used after the first development period.
  3. BF is lower, as it ignores reported claims in the projection.
  4. BF equals CL once the origin year is 50% developed.

Explanation

Bornhuetter-Ferguson adds expected unreported claims to reported claims, while chain ladder grosses up reported claims by the inverse of the development pattern. If reported claims are low relative to expectation, chain ladder gives a low ultimate, whereas BF retains expected claims for the undeveloped portion and is higher.

Question 25Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

What is superimposed inflation in general insurance claims reserving?

  1. The extra inflation that arises when nominal claim payments are discounted.
  2. The effect of volume weighting rather than simple averaging of factors.
  3. Cost growth above background inflation from claim behaviour or legal change. Correct answer.
  4. The expected increase in premium rates when renewal business is repriced.

Explanation

Superimposed inflation is the part of claims cost inflation not explained by background economic inflation. It can arise from social, legal, or behavioural changes and is often estimated separately in long-tail reserving.

Question 26Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

What does incurred but not enough reported (IBNER) represent in general insurance reserving?

  1. Claims incurred but not yet reported to the insurer.
  2. Claims reported but expected to close without payment.
  3. The part of the unexpired risk reserve relating to reported claims.
  4. Additional development on reported claims beyond the current case estimate. Correct answer.

Explanation

IBNER is the additional amount expected to be paid on claims already reported, over and above the current case reserves. It arises because case estimates are often initially inadequate and are strengthened as claims develop.

Question 27Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

When technical provisions are discounted, what is meant by the unwinding of the discount over time?

  1. The release of the risk margin as claims are settled.
  2. The rise in the liability as payment approaches due to time value. Correct answer.
  3. The adjustment made to development factors to remove historical claims inflation.
  4. The fall in the liability caused by expected claims inflation.

Explanation

Discounting reduces the liability to present value. As time passes and payment becomes closer, the present value increases at the discount rate; this accretion is called unwinding of the discount.

Question 28Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In an over-dispersed Poisson chain ladder model for claims reserving, what does the dispersion parameter capture?

  1. Correlation between origin years in the same calendar period.
  2. Bias introduced by using cumulative rather than incremental data.
  3. Variability of the development factors around their mean.
  4. Extra variance of incremental claims beyond the Poisson mean-variance link. Correct answer.

Explanation

In an over-dispersed Poisson model the variance of incremental claims is assumed to be the dispersion parameter times the mean. The dispersion parameter therefore captures variability beyond the Poisson mean-variance relationship.

Question 29Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

A reserving actuary is setting technical provisions for a liability line with a few very large claims. Which approach best addresses the instability caused by these claims in a chain ladder projection?

  1. Remove or separately project large claims and add an explicit loading. Correct answer.
  2. Include all large claims and rely on aggregate development factors.
  3. Increase the tail factor to reflect the large claims.
  4. Use only the latest origin year's development factor.

Explanation

A few large claims can distort aggregate development factors and make a chain ladder projection unstable. A common response is to remove them from the main triangle, project them separately, and add an explicit large-claim loading.

Question 30Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

When a bootstrap chain ladder method is used to estimate the predictive distribution of reserves, why are resampled pseudo-triangles generated?

  1. To eliminate parameter estimation error from the model.
  2. To reflect process variance and parameter estimation error in reserves. Correct answer.
  3. To convert incurred claims into paid claims.
  4. To ensure development factors equal their expected values.

Explanation

Bootstrap chain ladder resamples residuals to create pseudo-triangles, refits the model, and simulates reserves. This captures both process variance and parameter estimation error in the predictive distribution.

Question 31Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

Under a risk-margin technical provisions framework, which item is added to the best estimate of claims liabilities?

  1. A deferred acquisition cost asset
  2. A risk margin Correct answer.
  3. An allowance for future underwriting profit
  4. A provision for reinsurance commission

Explanation

Technical provisions are built from a best estimate of claims liabilities plus a risk margin. The risk margin compensates for the cost of holding capital against non-hedgeable reserve risk. It is not an asset, a profit allowance, or a reinsurance commission provision.

Question 32Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In general insurance reserving, what does reported but not settled, or RBNS, refer to?

  1. Claims reported to the insurer and still open Correct answer.
  2. Claims that have been paid but not yet closed in the system
  3. Claims that are closed with no payment
  4. Claims incurred but not yet reported

Explanation

RBNS claims are claims already notified to the insurer but not yet finally settled at the valuation date. They form part of the outstanding claims liability alongside IBNR. A paid claim is no longer an outstanding claim for reserve purposes.

Question 33Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

When is the pure expected loss ratio method most appropriate for estimating an origin year's ultimate claims?

  1. When paid and incurred triangles indicate a clear change in case reserving practice
  2. When claim counts are unavailable but average claim costs are highly stable
  3. When the origin year has a long and stable development history and tail factors are well determined
  4. When the year is immature and a credible expected loss ratio is available Correct answer.

Explanation

The pure expected loss ratio method applies a selected loss ratio to earned premium or exposure rather than relying on observed development. It is useful for immature origin years where development data are not yet credible but pricing and exposure information support a reliable loss ratio. A long development history would normally favour a development-based method.

Question 34Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In a cumulative paid claims triangle, two consecutive development factors for age 12 to 24 are 1.50 from origin year A with cumulative paid 1,000 at age 12 and 1.20 from origin year B with cumulative paid 4,000 at age 12. What is the volume-weighted development factor from age 12 to 24?

  1. 1.35
  2. 1.26 Correct answer.
  3. 1.50
  4. 1.20

Explanation

The volume-weighted factor sums next-age cumulative claims and divides by summed prior-age claims: (1,000 x 1.50 + 4,000 x 1.20) / (1,000 + 4,000) = 6,300 / 5,000 = 1.26. It gives more weight to the larger origin year.

Question 35Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

What is the main purpose of a tail factor in chain ladder reserving?

  1. To adjust development factors for reinsurance recoveries
  2. To convert an incurred triangle into a paid triangle
  3. To project development beyond the latest observed age Correct answer.
  4. To remove calendar-year effects from the triangle

Explanation

A tail factor extends the development pattern from the latest observed development age to ultimate. It captures expected further claim payments or incurred claim development after the triangle ends. It does not remove calendar-year effects, convert triangles, or adjust for reinsurance.

Question 36Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

A reserving actuary projects an ultimate claim count of 1,200 and an ultimate average cost per claim of 15,000. Claims paid to date are 4,000,000. Using a simple average cost per claim method, what is the outstanding claims reserve?

  1. 14,000,000 Correct answer.
  2. 18,000,000
  3. 22,000,000
  4. 4,000,000

Explanation

Ultimate claims equal expected claim count times expected average cost per claim: 1,200 x 15,000 = 18,000,000. The outstanding claims reserve is ultimate claims less claims paid to date: 18,000,000 - 4,000,000 = 14,000,000.

Question 37Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

A cumulative incurred triangle shows a negative incremental value in a recent origin year. Which explanation is most consistent with a genuine reserving phenomenon rather than a data error?

  1. The risk-free discount rate increased during the period
  2. Earlier case reserve strengthening has since been released Correct answer.
  3. The number of reported claims increased during the period
  4. The insurer wrote more premium in that origin year

Explanation

A negative incremental incurred value means cumulative incurred claims fell between valuations. This can happen when case reserves set too high in an earlier period are released as claims settle for less than expected. Changes in premium, claim count, or discount rate do not by themselves create a negative incurred claims increment.

Question 38Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

Which assumption is central to the basic chain ladder method for estimating ultimate claims?

  1. All origin years must have identical ultimate loss ratios
  2. Each origin year follows a common development pattern Correct answer.
  3. Paid and incurred claims must be projected separately
  4. Case reserves must equal ultimate claims at the latest valuation

Explanation

The basic chain ladder assumes that origin years share a common development pattern at each development age, after allowing for scale. Projected ultimates are derived by applying selected development factors to each origin year's latest cumulative claims. Identical ultimate loss ratios and adequate case reserves are not required assumptions.

Question 39Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

What problem does the Munich chain ladder method primarily address?

  1. Estimation of tail factors beyond the last observed development age
  2. Allowance for reinsurer default in recoveries
  3. Correlation between paid and incurred development Correct answer.
  4. Selection of the initial expected loss ratio in Cape Cod

Explanation

The Munich chain ladder method addresses correlation between paid and incurred development patterns, particularly when case reserves are strengthened or released. It uses information from both paid and incurred triangles to reduce the bias that can arise when the two bases imply different ultimates. Tail estimation, reinsurer default, and Cape Cod initial loss ratios are separate reserving issues.

Question 40Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

An insurer has two independent lines of business. The estimated standard deviation of reserves is 300 for line A and 400 for line B. Assuming independence, what is the standard deviation of total reserves?

  1. 100
  2. 500 Correct answer.
  3. 700
  4. 350

Explanation

For independent risks, variances add: total variance = 300 squared + 400 squared = 90,000 + 160,000 = 250,000. The total standard deviation is the square root of 250,000, which is 500. Adding the standard deviations directly would ignore diversification.

Question 41Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In general insurance reserving, what does the expected loss ratio represent?

  1. Ultimate claims divided by earned premium. Correct answer.
  2. Case reserves divided by the number of outstanding claims.
  3. Reported claims to date divided by earned premium for the same period.
  4. Paid claims divided by total admitted assets.

Explanation

The expected loss ratio is a projected ultimate claims ratio: ultimate claims cost divided by earned premium for the same exposure period. It is used as an a priori ratio in expected loss ratio and Bornhuetter-Ferguson reserving, not as a ratio of reported or paid amounts to premium.

Question 42Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

What is the primary purpose of a case reserve for a reported general insurance claim?

  1. To hold a margin for adverse deviation across the whole reserve portfolio.
  2. To provide for unexpired risks on policies still in force.
  3. To cover claims that have occurred but have not yet been reported.
  4. To record the current estimated cost of that individual claim. Correct answer.

Explanation

A case reserve is set claim by claim for a reported claim and reflects the claims handler's current estimate of its ultimate settlement cost. IBNR covers unreported claims, unexpired risk reserves cover future cover, and a risk margin is a portfolio-level prudential addition.

Question 43Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

What is an unexpired risk reserve intended to cover?

  1. The risk that reinsurance recoveries will not be collectible.
  2. The estimated cost of settling claims that have already been reported but are not yet paid.
  3. Expected excess claims and expenses over unearned premium on unexpired policies. Correct answer.
  4. Claims that have occurred but are not yet reported at the valuation date.

Explanation

An unexpired risk reserve is recognized when the expected claims and expense outgo on the unexpired portion of in-force policies exceeds the unearned premium available. It addresses future cover, not unreported past claims, reported outstanding claims, or reinsurance credit risk.

Question 44Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

How does the Cape Cod reserving method differ from the Bornhuetter-Ferguson method?

  1. Cape Cod ignores reported claims entirely, while Bornhuetter-Ferguson bases the estimate only on reported claims.
  2. Cape Cod estimates the expected loss ratio from the data; BF uses an external a priori. Correct answer.
  3. Cape Cod automatically produces a discounted reserve, while Bornhuetter-Ferguson automatically produces an undiscounted reserve.
  4. Cape Cod can be applied only to paid claims triangles, while Bornhuetter-Ferguson can be applied only to incurred claims triangles.

Explanation

The Cape Cod, or Stanard-Bühlmann, method estimates the expected loss ratio from the insurer's own reported experience adjusted for development and exposure. Bornhuetter-Ferguson starts with an externally supplied a priori loss ratio and blends it with reported claims.

Question 45Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

What does the Mack chain ladder model add to the standard chain ladder point estimate?

  1. An estimate of the reserve's standard error. Correct answer.
  2. A method for adjusting the data for superimposed inflation.
  3. A method for selecting an appropriate tail factor.
  4. A procedure for estimating claims handling expenses.

Explanation

The Mack chain ladder model adds a distribution-free estimate of prediction error, often expressed as the standard error or coefficient of variation of the reserve. It does not select tail factors, adjust for superimposed inflation, or estimate claims handling expenses by itself.

Question 46Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In technical provisions presented gross of reinsurance, how are expected reinsurance recoveries on incurred claims normally treated?

  1. Recognized as a separate asset, subject to a collectibility assessment. Correct answer.
  2. Included in the risk margin rather than in the best estimate.
  3. Excluded entirely because reinsurance is not part of technical provisions.
  4. Deducted from the gross best estimate to produce a net technical provision.

Explanation

When technical provisions are presented gross of reinsurance, the gross liability is recognized in full and expected reinsurance recoveries are shown separately as an asset. That asset is assessed for collectibility and counterparty default risk; deducting it would produce a net rather than gross presentation.

Question 47Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In the standard chain ladder method, how is a development factor for age k to k+1 typically calculated?

  1. The most recent origin year's individual link ratio applied to all years.
  2. Summed later-age cumulative claims divided by summed earlier-age cumulative claims. Correct answer.
  3. The median of each origin year's individual link ratio.
  4. The unweighted simple average of each origin year's individual link ratio.

Explanation

The standard chain ladder development factor is volume-weighted: it divides the sum of cumulative claims at the later age by the sum at the earlier age across the origin years used. This gives more weight to larger origin years than a simple average or median of individual link ratios.

Question 48Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

A claims development triangle shows that paid claim amounts for many origin years increased sharply at the same calendar date. Which explanation is most consistent with this pattern?

  1. A change in the ultimate loss ratio assumption for the most recent origin year only.
  2. A calendar-year effect such as inflation or a legal change. Correct answer.
  3. Random process variance confined to one origin year.
  4. A tail factor that is too low for the oldest origin year.

Explanation

A diagonal pattern, with several origin years affected at the same calendar date, points to a calendar-year influence such as claims inflation, a legal change, or a shift in claims handling. Origin-year-specific assumptions or tail factors would not normally create a common calendar-date movement across many origin years.

Question 49Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

In stochastic claims reserving, which statement best distinguishes process variance from parameter uncertainty?

  1. Process variance can be eliminated by collecting more data; parameter uncertainty cannot be reduced at all.
  2. Process variance arises only from discounting; parameter uncertainty arises only from inflation.
  3. Process variance applies only to reported claims; parameter uncertainty applies only to IBNR.
  4. Process variance is the randomness of claim outcomes; parameter uncertainty concerns estimated model parameters. Correct answer.

Explanation

Process variance is the natural variability of individual claim outcomes even if the model and parameters were known. Parameter uncertainty is the uncertainty in estimating those parameters from limited data; more data reduces parameter uncertainty but does not remove process variance.

Question 50Reserving for general insurance liabilities (technical provisions, claims development, reserving methods and uncertainty)

Which practice best monitors whether a reserving methodology has produced reliable ultimate estimates over time?

  1. Recalculating the risk margin using a higher cost-of-capital rate.
  2. Back-testing past ultimate estimates against subsequently emerged claims. Correct answer.
  3. Selecting the methodology that produces the lowest reserve estimate at each valuation date.
  4. Applying only the most recent origin year's development factor to every origin year.

Explanation

Back-testing compares previously selected ultimate estimates with the claims that actually emerged for the same origin years, revealing bias and instability in the method. Choosing the lowest estimate, changing the risk margin, or applying one development factor to all years does not test predictive reliability.