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Free Study Materials for the Casualty Actuarial Society (CAS) Exam 5B 

(Old Exam 6)

Section 5

Basic Concepts Regarding Data Aggregation and Other Data Treatments in Unpaid Claim Estimation: Practice Questions and Solutions

G. Stolyarov II
July 8, 2010 - Republished July 11, 2014
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This section is part of Mr. Stolyarov's Free Study Materials for the CAS Exam 5B.

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Estimating Unpaid Claims Using Basic Techniques, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5B (Old Exam 6). Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Friedland, Jacqueline F. Estimating Unpaid Claims Using Basic Techniques. Casualty Actuarial Society. July 2009. Chapters 3-5, pp. 34-52.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S6-5-1. What are the three possible treatments of allocated loss adjustment expenses (ALAE) in excess-of-loss reinsurance contracts? (See Friedland, p. 34.) Which of these is the most common treatment?

Solution S6-5-1. The following are the three possible treatments of allocated loss adjustment expenses (ALAE) in excess-of-loss reinsurance contracts (Friedland, p. 34):

1. All ALAE are included in the claim amount for the purposes of determining whether reinsurance coverage applies. This is the most common treatment.

2. All ALAE are excluded from coverage.

3. ALAE are included on a pro rata basis. The amount of ALAE covered is the total ALAE multiplied by the ratio of the excess amount of the claim to the total claim amount.

Problem S6-5-2.

(a) What is the most common type of exposure base for insurers?
(b) For self-insurers, what are three possible alternative exposure bases if the exposure base in part (a) is not available? For each alternative, identify a type of insurance to which it would apply. Why would such alternatives be necessary?

Solution S6-5-2. This question is based on the discussion in Friedland, p. 35.

(a) The most common exposure base for insurers is earned premium.

(b) Self-insurers most often do not pay premiums, so alternative exposure bases are needed. The following exposure bases are described by Friedland, p. 35:

1. Number of employees - for crime insurance
2. Property values - for property insurance
3. Number of vehicles - for automobile liability insurance
4. Miles driven - for automobile liability insurance
5. Payroll - for workers' compensation insurance in the U. S.
6. Sales - for general liability for corporations
7. Square footage - for general liability for corporations
8. Population - for general liability for public agencies
9. Operating expenditures - for general liability for public agencies
10. Outpatient visits - for hospital professional liability
11. Average occupied beds - for hospital professional liability

Any three of the above suffice as an answer. Other valid answers may also be possible.

Problem S6-5-3. According to Friedland, p. 37, what are the four elements that a data review may examine to "verify that the data utilized are reliable and sufficient for the intended purpose"?

Solution S6-5-3. The following four elements are mentioned by Friedland, p. 37:

1. Consistency with prior data
2. Data definitions
3. Consistency with financial statement data
4. Data reasonableness

Problem S6-5-4. For each of the following methods of aggregation, give (i) an advantage and (ii) a disadvantage of the method. (See Friedland, pp. 40-43.)

(a) Calendar year aggregation
(b) Accident year aggregation
(c) Policy year aggregation
(d) Report year aggregation

Solution S6-5-4.

(a) Calendar year aggregation

(i) Advantages (any one is acceptable):
1. No future development exists; data remain fixed at the end of the calendar year.
2. Data are easily available from insurers' financial reports.
(ii) Disadvantages (any one is acceptable):
1. The issue of development cannot be addressed.
2. Mismatch between premiums and losses (the premiums collected during a year do not necessarily pertain to the policies on which losses have occurred, and vice versa).

(b) Accident year aggregation
(i) Advantages (any one is acceptable):
1. Easy to understand and produce
2. Shorter typical development timeframes than for the policy year method
3. Claims can be tracked by accident year so as to detect changes in economic and regulatory factors or major claim events.
4. Many industry benchmarks based on accident year data exist.
(ii) Disadvantages (any one is acceptable):
1. There is still a possible mismatch between claims and exposures.
2. This method might include claims from policies issued and priced at fundamentally different times.
3. Can "mask changes in retention levels" for self-insureds with high deductibles (Friedland, p. 41).

(c) Policy year aggregation
(i) Advantages (any one is acceptable):
1. Match between claims and exposures.
2. Useful for tracking effects of underwriting or pricing changes.
3. Useful for data pertaining to self-insureds to whom only one policy applies.
(ii) Disadvantages (any one is acceptable):
1. Lengthy development timeframe and difficulty of quickly estimating ultimate claims.
2. Difficulty in isolating and comprehending the effect of a major court ruling, catastrophe, or similar large event.

(c) Report year aggregation
(i) Advantages (any one is acceptable):
1. Stability of data and development patters that are relatively easy to determine
2. No need to estimate reported claims
3. Particularly useful for claims-made policies
(ii) Disadvantage (others may be possible):
1. Pure IBNR (incurred but not reported) cannot be estimated at all, so additional methods for estimating it may be required.

Problem S6-5-5. Name two situations in which an insurer's claim development triangle might show negative claim development over time. (See Friedland, p. 52.)

Solution S6-5-5. The following are situations in which an insurer's claim development triangle might show negative claim development over time:

1. The insurer has settled some claims for less than prior case outstanding estimates.
2. The insurer has included recoveries (e.g., salvage and subrogation) with the claim data, meaning that any recovery that occurs would reduce the net amount paid on the claim.

Gennady Stolyarov II (G. Stolyarov II) is an actuary, science-fiction novelist, independent philosophical essayist, poet, amateur mathematician, composer, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. 

In December 2013, Mr. Stolyarov published Death is Wrong, an ambitious children’s book on life extension illustrated by his wife Wendy. Death is Wrong can be found on Amazon in paperback and Kindle formats.

Mr. Stolyarov has contributed articles to the Institute for Ethics and Emerging Technologies (IEET), The Wave Chronicle, Le Quebecois Libre, Brighter Brains Institute, Immortal Life, Enter Stage RightRebirth of Reason, The Liberal Institute, and the Ludwig von Mises Institute. Mr. Stolyarov also published his articles on Associated Content (subsequently the Yahoo! Contributor Network) from 2007 until its closure in 2014, in an effort to assist the spread of rational ideas. He held the highest Clout Level (10) possible on the Yahoo! Contributor Network and was one of its Page View Millionaires, with over 3.1 million views. 

Mr. Stolyarov holds the professional insurance designations of Associate of the Society of Actuaries (ASA), Associate of the Casualty Actuarial Society (ACAS), Member of the American Academy of Actuaries (MAAA), Chartered Property Casualty Underwriter (CPCU), Associate in Reinsurance (ARe), Associate in Regulation and Compliance (ARC), Associate in Personal Insurance (API), Associate in Insurance Services (AIS), Accredited Insurance Examiner (AIE), and Associate in Insurance Accounting and Finance (AIAF).

Mr. Stolyarov has written a science fiction novel, Eden against the Colossus, a philosophical treatise, A Rational Cosmology,  a play, Implied Consent, and a free self-help treatise, The Best Self-Help is Free. You can watch his YouTube Videos. Mr. Stolyarov can be contacted at

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