Insurance Case Studies

Introduction to Case Studies

• This chapter uses case studies to apply general insurance knowledge to specific situations.
• The case studies do not introduce new technical concepts but demonstrate how to apply prior knowledge, especially higher-order skills like analysis and judgment.
• Each study includes a scenario, initial thoughts, answer development, a skeleton plan, SA3 skill considerations, and an example solution.
• Effective study involves multiple sessions: initial scenario review, idea generation, reflection, plan refinement, exam solution practice (30-40 minutes), and comparison with given solutions.
• Solutions are realistic illustrations and not exhaustive; alternative ideas may be valid.
• The goal is to think through issues, not memorize a model answer, emphasizing the application of comprehension to practice.
• Time can be saved in exams using shorthand, and this is done in the document for planning purposes
• Abbreviations are fine if they appear in Core Reading, but should be avoided otherwiae
• Examples of shorthand: PD for property damage, BI for bodily injury, and ACPC for average cost per claim.

Case Study Overviews

• Case Study 1 is adapted from a 1988 Subject 9A exam question, worth 30 marks, focusing on 'answering' skills and is segmented into shorter questions.
• A suggested 'planning target' is around 20 minutes, but actual exam planning might take up to 50% of the time.
• Case Study 2 gives a reinsurance pricing scenario with minimal detail, necessitating unique problem-solving approaches, with 30 minutes of plan time considered appropraite.
• Case Study 3 addresses long-term, strategic decisions resembling those of a management board, with consideration on mergers and company improvements.
• Case Study 3 uses a past SA3 exam question with fewer marks, suggesting 30-40 minutes but offers a chance to prioritize key issues due to the nature of the complex problems.
• Case study 3 if this was an exam question may be work up to 50 marks

Scenario Context

• A UK general insurance company estimates outstanding claim reserves on December 31 each year using various statistical methods, adjusting the method, data, or both if assumptions are invalid.
• For private motor business, reserves are estimated using inflation-adjusted chain ladder and average claim size methods.
• Preparation should involve describing adjustments and outlining preliminary investigations when dealing with unusually icy weather, gradual movement towards higher car ratings, claims recorded as settled after 12 months without activity due to a new system, and a new sales tax increasing property damage claims by 15%.

Actuarial Considerations

• Reserving questions should be approached with key ideas from Subject SP7 Chapters 14 and 15.
• Key points should include data groupings, data choice, treatment of large losses/catastrophes/non-standard risks, business basis, development pattern consistency, projection methods, assumption and recoveries.
• A checklist of general concepts important in reserving should be made
• Details to look out for include; outstanding claims reserves (IBNER and IBNR case estimates, prudence), statistical methods (chain ladder, BF, bootstrapping), assumptions (fully run-off, past as a good predictor), data (groupings, heterogeneity, accuracy), and comprehensive private motor business (level of cover, claims characteristics).

Claims Characteristics

• Mental image of the claims characteristics should be formed when mentioning a class of business.
• Claim characteristics can be: claim type (PD and BI), distribution over the calendar year of occurrence, distribution over their tail of settlement, and industry changes like LASPO.

Reserving Methods

• There are two reserving methods: inflation-adjusted chain ladder and average claim size.
• The inflation-adjusted chain ladder method ignores number of claims but recognizes inflation changes (with other calendar year effects).
• The average claim size calculates numbers of claims times expected claim size and has a separate extraction of trends in claim size and frequency.
• Both methods use cumulative data.
• Patterns of the numbers or amounts of claims and how and the extend inflation affects them are basic assumptions.
• Assumptions might not stand due to changes in business mix, the way you handle claims, or external factors (judicial inflation and claim propensity).

Addressing Question Requirements

• The important adjustments, preparatory investigations and covering the methods and the data.
• Bring together preliminary thoughts to deduce if and how each method is affected to reduce corruption by problems.
• Be sure that some are only slightly distorted, identifying processes that aren't a major distraction from the main investigation.
• Calm down from several minutes of absorbing specific problems, but keep an eye on the clock.

Planning The Response

• Take an account of what you want to say and prioritise those to develop a detailed response, using coherent thoughts.
• The motor claims split into several categories and is determined on why you require to divide them and the least level that you should choose.
• The PD and BI data between claims is important between these
• What, where, why / how questions are important for scoring
• PD claims are shorter and are more effective when trying to score marks
• Consider each years effect on the claims with the effect on those years
• With the unusual even effects PD claims the claim estimates will need to be based on PD and BI to not distort it, and be sure to whether the values would be an overestimate or udnerestimate.
• But what about claims estimates for future accident years? We're told that an additional number of PD claims occurred early this year. We can expect these to be settled quickly, certainly before the year end. As a result, (total) claim amounts settled this year will be unusually high. This will in turn cause a bulge in the estimated payments in the following years, because the chain ladder method will project the increased amounts of payments forward and thus assume it's a regular feature. Again we wonder what the effect of this will be. We think that future reserving exercises (ie for future accident years) will end up underestimating the amounts of outstanding claims, since the development for the current accident year will be faster than normal.

Methods

Inflation Adjusted Chain Ladder Method

• Initial thought was that PD claims are short-tailed, so there won't be much inflation to worry about. But wait a minute, the inflation assumption is just one aspect of this method. Another key assumption is that the (real) development pattern remains stable over time. All of the ideas we've thought about above will distort the development pattern, whether they're real or not. So our initial thought was wrong, we do need to talk about this method.

Average Cost Per Claim Method

• The question talks about claim numbers, so we're bound to have to concentrate on the average cost per claim method, right? But hang on again, we're told the calculation is based on a multiple of outstanding claims, and the icy weather claims will very nearly all be settled by the year end.
• So again our initial thought was wrong, we don't need to talk about this method much. We think we should still mention it though, to show we understand the concept. Besides, we know that one of the pitfalls in the Subject SA3 exam is that of being too categorical, after all there are bound to be a few claims still open so we don't want to ignore these entirely.

Adjustments

• Next, we have to decide how to overcome these problems.
• We remember this part of our answer should include investigations as well as adjustments. Since we've realised the average claim severity might not be distorted (or at least, not by much), our answer for this method will be mostly checking and investigating effects, rather than proposing adjustments.
• One approach we could use for the ACPC method would be to first identify the number of claims that are outstanding at the year end, and estimate how big an excess this is over the 'normal' number. We could estimate this from earlier years' experience (assuming that earlier years' experience is still representative). Finally, average claim size factors could be estimated, maybe using sampling techniques say. These 'average factors' must be chosen carefully - they may be larger than the factors derived from the average cost per property damage claim in the previous year.
• Mind you, we don't need to think too hard to imagine that we'll end up splitting out the icy weather claims for the inflation-adjusted method. We noted this in our initial thoughts, and besides we know that's what insurers do in practice. So we could suggest that for the ACPC method too. But we're getting ahead of ourselves, so we should talk about the ACPC method second. In fact that's great, it means we'll talk about the biggest problem first.
• Now for the inflation-adjusted method.
• We have established that we need to separate out PD claims from other types of claim. However, it will not be sufficient for us simply to apply the chain ladder method directly to PD claims, because there will still be different patterns of occurrence dates in the current year relative to earlier years. But, what we can do is try to group the data even further, into quarterly origin periods, or even monthly origin periods.

Advantages

• Weknow that this level of groupingis used alot for motor business, so the advantages should outweigh the disadvantages:

• Further groupings will prevent the extra February claims from distorting the projected development of whole future years-Volumes of business are generally high enough for motor business for the data to still be credible. However, the problem will not be removed entirely.

OR

• Alternatively, we could remove the extra February claims from the data. To do this, we would need to identify all the February property damage claims, and the total amount paid to datein respect of them. Hopefully the claims database will allow us to do this. We can then project the remaining claims as normal.
• Thisis probably the mostlikely option so we make a note to say so, since weknow the examiners will want usto show this sort of practical awareness.
• But we need to remember to talk about investigations as well as adjustments. Weshould check whether this years February (excluding the extra claims) is anormal February, to say whether anyfurther adjustments are required to the remaining data. A high-level check would beto compare the projection to the corresponding results from previous accident years. If the checkis satisfactory, it only remains to add on an allowance for the extra payments.
• Wait a minute, weve thought about anormal February already, when we were thinking about the average cost per claim method. So we need to be careful not to repeat ourselves here.
• Now we need to deal with the extra payments separately. It seems likely that there are no IBNR claims for this event, so we need only worry about outstanding reported claims. Weshould probably check this though, so we need to say well do that. An analysis ofreporting delays would help, although this as aless significant issue so it will depend on the amount of time we have for the reserving exercise.
• For high volume business such asthis, it is likely that the case estimates heldin the claims database are generated automatically. This meansit might be too simplistic just to set the reserve equal to the sum of the case estimates, particularly because any claims still outstanding might be more complex than average. Wecould sample from the outstanding icy weather claims files, but it will take statistical skill in selecting an unbiased sample from the extra cases. We should also talk to the estimators, astheir skill will be needed to come up with estimates wecan rely on.
• A quick glance at our initial thoughts reminds us that we need to allow for recoveries from other insurers and reinsurers, as these maystill be outstanding, despite the fact that claims have been paid to the policyholder. We wonderif well have to talk about recoveries for all scenariosin the question. We wantto avoid sounding repetitive.

Second Part

• We dont know when/why to state assumptions so you must check data for proof needed
• You must look for what has happened for the last the three years
• To check whether different rating groups experience different claims development
• This method projects claim frequency and claim severity separately
• We can expect higher risk groups when analysing trends for what to look for
• Higher rating group costs increases the cost due to the car being heaveier/faster
• Damage occurs due to younger driver and limited safety
• The trend that needs to be collected needs statistical evidence

New Administration

• To avoid repeating its important to not repeat info used that wasn't working previously so you won't get the marks.
• Subdivide each data if necessary to get it to work
• Oh No! Make sure to create structure in each of your sections to limit using repeated arguments and wasting time

New System

• Don't use the inflation-adjusted method, it doesn't use claim numbers.
• Wont effect aggregate
• We're toold this method is bassed on the number of outstanding, bur there will be claims
• Is there any extra stuff that might change? Maybe deduct the payments
• See whether the system can do it easily.
• If past system will be out we can change those to new data to be on a more consistent style

The Main Idea

• Must keep data on a consistent basis
• Check with database on 'as-if' to allow database to re-access historical documents

The New Addition

• Always provide cons and pros for each method used, but keep in mind that the new method might be risky
• We're glad that these issues are being thought of to confirm how well structure it Reaffirm why PD claims are only connected to the insurers property
• Alts you can just adjust the data
• Consisntey should be driving the main goal in this
• Adjust previous payment for the last year and allow all date to act as the salestax has always applied

The Claim

• The amount will average over the tax, so these adjustments will be more complicated.

Other

• 10 marks
• This has shown what each method relies on and has used all sections with the new info provided and has given lots of details needed. This is why the process is needed so there isn't an accident or tangent

Show Judgement

• We need to show how we can slot that data in with what happened.

Specimen Solution

• Property damage occurs and is separate for these
• This allows how what data will change that shows it is correct and can separate sections if need.

Icy Weather

• Have that data if need but if not don't to provide accuracy

• Have past reports data for reference on if can make this work

• This will see what can change for better

• Now lets have the current claim value

The Data

• See if data can be adjusted
• You wont show the previous method but make the correct one the more evident one.
• Don't change to get higher value of something but to have similar stuff is more useful to make the process easier and correct