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

(Old Exam 6)

Section 1

Basic Concepts Regarding Unpaid Claim Estimation: Practice Questions and Solutions

G. Stolyarov II
July 5, 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.

Formula for This Section

Formula 1.1: Reported claims = paid claims during period + case outstanding at end of period - case outstanding at beginning of period

The above formula applies to incremental reported claims -- i.e., reported claims applicable to a particular time period, irrespective of what happened during prior time periods.

Friedland, Jacqueline F. Estimating Unpaid Claims Using Basic Techniques. Casualty Actuarial Society. July 2009. Chapters 1 and 2, pp. 1-24.

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

Problem S6-1-1. Friedland (p. 9) discusses two ways to categorize claim adjustment expenses: (1) allocated versus unallocated loss adjustment expenses (ALAE vs. ULAE) and (2) defense and cost containment versus adjusting and other expenses (DCC vs. A&O). For each of these classification systems, define the two categories of expenses.

Solution S6-1-1.

Allocated loss adjustment expenses (ALAE): Costs that can be assigned to the adjustment of a particular claim.

Unallocated loss adjustment expenses (ULAE): Costs that cannot be easily assigned to a particular claim - such as the insurer's rent, payroll, and computer expenses.

Defense and cost containment (DCC) expenses: All medical cost containment and defense litigation expenses.

Adjusting and other expenses: All claims adjusting expenses, whether or not they can be attributed to an individual claim.

Problem S6-1-2.

(a) What is the difference between an "unpaid claim estimate" and a "reserve" as officially defined in Actuarial Standard of Practice (ASOP) 43? (See Friedland, p. 13.)

(b) What is the difference between an "unpaid claim estimate" and a "carried reserve"? (See Friedland, p. 14.)

Solution S6-1-2.

(a) ASOP 43 confines the term "reserve" to "an amount booked in a financial statement." An "unpaid claim estimate" is an actuarial estimate of future payment obligations resulting from claims arising out of already occurred events.

(b) An "unpaid claim estimate" arises out of the use a particular method of estimation, and different methods can produce different estimates. A "carried reserve" for unpaid claims is the amount which is actually reported or published in the relevant financial statement.

Problem S6-1-3. List the five components of an unpaid claim estimate (discussed in Friedland, p. 14). Which of these constitute the broad term "incurred but not reported" (IBNR)?

Solution S6-1-3. According to Friedland, p. 14, the following are the five components of an unpaid claim estimate:

1. Case outstanding on known claims = Unpaid case

2. Provision for future development on known claims

3. Estimate for reopened claims

4. Provision for claims incurred but not reported

5. Provision for claims in transit = claims reported but not recorded

The term IBNR refers to items 2 through 5 above - i.e., every category except case outstanding on known claims.

Problem S6-1-4. Define the following dates related to insurance claims, described by Friedland (p. 22):

(a) Policy effective date

(b) Accident date

(c) Report date

(d) Transaction date

(e) Closing date

(f) Reopening date

Solution S6-1-4.

(a) Policy effective date: Date the insurance policy is issued.

(b) Accident date: Date of occurrence of covered loss.

(c) Report date: Date of insurer becoming notified of the claim.

(d) Transaction date: Date on which a payment is made or a case outstanding transaction occurs.

(e) Closing date: Date of either initial or final closure of the claim.

(f) Reopening date: Date on which an insurer begins to consider a previously closed claim open.

Problem S6-1-5. The case outstanding at the end of the year 2015 is $321,031. At the beginning of 2015, the case outstanding was $346,120. Paid claims during 2015 were $120,315. What is the dollar amount of reported claims during 2015? (See Friedland, p. 24.)

Solution S6-1-5. We use the formula
Reported claims = paid claims during period + case outstanding at end of period - case outstanding at beginning of period = 120315 + 321031 - 346120 = $95,226.

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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