Chapter 22: Reserving

Question 1

What is the ‘once and once-only’ principle in reserving for benefits? (1)

According to the profitability principle, when is the profitability of a product known with certainty? (1)

What is the fundamental equation of the balance sheet principles? (1) Under the balance sheet principles, what happens when the value of Assets minus Liabilities (A-L) decreases? (1)

How do reserves influence the release of profits according to the profitability principle? (1)

Answer 1

1. All liabilities must be covered without any double-counting.
2. It is only known with certainty once the last benefits and premiums have been paid.
3. Assets (A) = Owners’ Equity (OE) + Liabilities (L). A loss or strain emerges
4. Reserves have a second-order effect, influencing the timing of when profits are released.

Question 2

How is the Gross Premium Prospective Policy Value (GPPPV) calculated?

Answer 2

{EPV of future claims} + {EPV future expenses} – {EPV of future premiums}

Question 3

For products with a term of one year or less, what reserve is used instead of the GPPPV? And why? (1)

Answer 3

The higher of the Unearned Premium Reserve (UPR) or the Unexpired Risk Reserve (URR).
where URR is calculated by applying the projected loss ratio to the premium and Additional Unexpired Risk Reserve (AURR) is the top-up amount needed on the UPR to
equalise the URR and UPR: AURR=max{URR−UPR,0}

The shorter period makes monthly approximations for mortality and morbidity inaccurate.

Question 4

For monthly premium products like PMI, why would the reserve for claim events that have not yet happened typically be small or zero?

Answer 4

Because premiums are paid monthly, closely matching the short-term risk exposure. (money in immediately goes out)

Question 5

What is the purpose of a option reserve, mismatching reserve, equalisation reserve, catastrophe reserve?

Answer 5

1. These are held to fund policy options.
2. It is held when the assets do not match the liabilities and may be required by regulation.
3. It is held rom profitable years to smooth profits, contributions, or premiums over time.
4. Funds are held aside in case of a catastrophe.

Question 6

The Two primary methods of calculating reserves

Answer 6

1. Case estimates (after claim event is reported)
   The ultimate value of a claim is decided by specialist expertise or judgement.

Adv
- add value for LTCI and PMI because of the large or unusual claims

Disadv
-Costly
- Dont add value when there is no uncertainty regarding the benefit amount
- Not practical for CI products due to large claim volumes

2. Statistical estimates (before claim is reported)

Adv
- Used where data is relatively homogeneous and experience is stable.
- Used for policy values and IBNR claims

Disadv
- tradeoff between stability and accuracy

Question 7

When coming up with case estimates, the case manager needs to consider (7):

Answer 7

Procedure type (keyhole vs open surgery)
Hospital or healthcare facility
Name of Principal Medical Practitioner
Policy coverage
Age, gender and past claims history
Current levels of medical inflation

Question 8

What are four typical adjustments made to data used for statistical estimates?

Answer 8

Claims inflation and settlement expenses
Expected reinsurance recoveries
Hospital discounts
Deductibles.

Question 9

What is a ‘claim cohort’ in the context of statistical reserving?

Answer 9

A group of claims defined by the same origin period, such as
- policy period
- treatment period
- period when claim event was reported

Question 10

Different statistical estimate approaches will give different results due to:

Answer 10

Adjustments for past inflation
Sensitivity to data anomalies
The choice of claim cohort
The choice of different development ratios or different grossing up factors
The choice of exposure and loss ratio to apply

Question 11

Point estimate of reserves methods (6):

Answer 11

1. Average cost per claim (ACPC)
   - frequency and severity are estimated separately
   - Reserve for claims outgo = average cost per claim x estimated ultimate number of claims - developed claims
   - relies on industry or reinsurer’s data
2. Loss ratio method
   - It is the cost of claims per unit exposure, premium or per life per month (PLPM) measure.
3. Basic chain ladder
   - Assumption: for each origin period, the expected value of claims in nominal terms, developed in each development period, is a constant proportion of the total claims, in nominal terms, from that origin period
4. Inflation adjusted chain ladder
   - is applied to past claims data, and to inflate projected claims to the
   expected development.
   - npt useful for health and care products because:
   + claims inflation does not occur between the treatment date
   and the development date
   + There is no need to adjust claim amounts between origin periods as any increase in underlying claims costs for a cohort of claims is already reflected in the developed claims for that cohort
5. BF Method (blends loss ratio and chain ladder)
   - adds more stability against the distortions in the development pattern
6. Cape Cod (extends the BF method)
   - Cape Cod Method derives an a priori ultimate loss
   ratio to be used in the BF method.
   * The claim reserve is found by taking the claims developed to date and dividing by a unit of
   exposure to obtain a loss estimate for each origin period
   * The a priori loss ratio is determined using fully developed internal claims data, weighted by
   exposure and percentage of claims developed. This provides greater weight to historical
   experience over recent experience.

Question 12

Distribution of reserves methods (2)

Answer 12

1. ACPC
   - Fit a joint distribution to claim frequency and severity.
2. Mack method
   - Development ratios and ultimate development factors are analysed to estimate the variability of development patterns and given a statistical distribution without requiting parametric assumptions.
   - uses bootstrapping

Question 13

What are some advantages and disadvantages of the Chain Ladder method?

Answer 13

Advantages
* The method is flexible and can be easily used to estimate the number of claims for the ACPC method.
* It is simple.
* Data distortions can be easily spotted in the incremental triangle.
* The result is easy to tie back to the cumulative distribution function of claims development.
* It forms the basis for blends and extensions, which can address some of its shortcomings.

Disadvantages
* Anomalies may be difficult to remove, for example, adjusting for a period with no claims development.
* If anomalies are not removed, the results are easily distorted.
* The method is inappropriate if current and historic claims development patterns differ.
* Changes to internal processes can create distortions.
* Tail factors may be difficult to estimate if no fully developed cohort is available.
* These anomalies may be difficult to remove.
* The results are easily distorted if anomalies are not removed.
* The method is inappropriate if the current and historic claims development patterns differ.
* Changes to internal processes can create this sort of distortion.
* Tail factors may be difficult to estimate if no fully developed cohort is available.

Question 14

Explain the Extended Average Cost Per Claim (EACPC) method as a blend of techniques.

Answer 14

The Extended ACPC can be blended with chain ladder methods or the BF method. For example, one can use the BCL or BF method to estimate ultimate claims, the value for which is then divided by expected claims numbers, possibly derived the same way, to obtain an average cost per claim.

Question 15

Describe the Bornhuetter-Ferguson (BF) method and its core concept.

Answer 15

The BF method combines the estimated loss ratio with a chain ladder method - usually the BCL. Therefore it improves on the crude use of a loss ratio by taking account of the information provided by the latest development data. Likewise, the addition of the loss ratio to a projection method serves to add some stability against distortions in the development pattern. As the final estimate of the ultimate loss is based on observed data and an initial estimate ignoring the observations, this method could be viewed as using a Bayesian approach. The loss ratio represents the eventual claims outgo, from paid claims, but the BF method can use claims reported, claims accepted, or claims paid data.

Steps:
Step BF1: Determine the initial estimate of the total ultimate claims from each treatment month using premiums and initial, prior or a priori, expected loss ratios.

Step BF2: Carry out BCL Steps 1–5 (given in Section 7.4) to estimate the proportion outstanding (1 – 1/fj). This is multiplied by the a priori ultimate paid claims estimates obtained in Step BF1 to give an estimate of the reserve amount for each origin period.

Question 16

What is the purpose of Bootstrapping in the context of claims reserving?

Answer 16

Bootstrapping allows this technique to be used without requiring explicit parametric assumptions. Bootstrapping is formally known as repeated resampling with replacement and can be used to turn a handful of data points into a complete distribution. The bootstrapped approach has five steps, involving using BCL or BF on an expected run-off triangle, taking the actual run-off triangle, applying an adjustment to the raw residuals, resampling these residuals, and applying chain ladder techniques to each alternative reality run-off triangle to obtain a distribution of reserves

Question 17

Briefly explain the Cape Cod method.

Answer 17

The Traditional Cape Cod method is also known as the Stanard-Bühlmann method. Under the BF method, an a priori ultimate loss is used in Step BF1. The Cape Cod method uses a specific technique to derive this estimate, which is then used to calculate the reserve in Step BF2. Under the Cape Cod method, the claims reserve is found by taking the claims developed to date and dividing by a unit of exposure to obtain a loss ratio for each origin period.