Actuarial Reserving Definitions and Principles: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of the Statement of Principles Regarding Property and Casualty Loss and Loss Adjustment Expense Reserves, 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. This is meant to give the student practice in answering questions of the format that will appear on 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.

Sources:
Casualty Actuarial Society, Statement of Principles Regarding Property and Casualty Loss and Loss Adjustment Expense Reserves, May 1988. pp. 10-14.

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

Problem S6-7-1.

(a) How does the Statement of Principles Regarding Property and Casualty Loss and Loss Adjustment Expense Reserves (hereafter, Statement of Principles) distinguish between a carried loss reserve and an indicated loss reserve? Which of these two is/are likely to change over time?

(b) The Statement of Principles (p. 11) describes a division that is often made between two different kinds of reserves. What is this division?

Solution S6-7-1.

(a) According to the Statement of Principles (p. 11), the carried loss reserve "is the amount shown in a published statement or in an internal statement of financial condition. An indicated loss reserve "is the result of the application of a particular loss reserving evaluation procedure." The indicated loss reserve will likely change over time.

(b) The division is between (1) reserves for claims that are known and (2) reserves for claims incurred but not reported (IBNR).

Problem S6-7-2.

(a) What is the difference between the case reserve and the reserve for known claims, as defined in the Statement of Principles?

(b) How does the Statement of Principles define a formula reserve?

Solution S6-7-2.

(a) According to the Statement of Principles (p. 11), the case reserve is "the sum of the values assigned to specific known claims", whereas the reserve for known claims consists of the case reserve and a "provision for future development on known claims", which a case reserve would lack.

(b) According to the Statement of Principles (p. 11), a formula reserve is a reserve "established for groups of claims for which certain classifying information is provided." As the name suggests, a formula is applied to determine reserve estimates for any claim in a group of claims with similar characteristics.

Problem S6-7-3. Briefly describe each of the three different kinds of development mentioned in the Statement of Principles (pp. 11-12).

Solution S6-7-3. The following three kinds of development are mentioned in the Statement of Principles:

1. Development in the number of reported claims for losses within a particular calendar period: More claims may get reported pertaining to the time period in question - even after that time period expires.

2. Paid development: Payments accumulate on particular claims over time.

3. Incurred development: The "difference between estimates of incurred costs at two valuation dates for a defined group of claims" (Statement of Principles, p. 12).

Problem S6-7-4.

(a) Fill in the blank: According to the Statement of Principles (p. 13), an actuarially sound loss reserve is supposed to estimate __________.

(b) If there is a range of actuarially sound estimates, the Statement of Principles (p. 13) articulates that the most appropriate estimate within this range is dependent on two criteria. What are these criteria?

Solution S6-7-4.

(a) According to the Statement of Principles (p. 13), an actuarially sound loss reserve is supposed to estimate "the unpaid amount required to settle all claims, whether reported or not, for which liability exists on a particular accounting date."

(b) If there is a range of actuarially sound estimates, the two criteria for selecting an estimate within the range are (1) "the relative likelihood of estimates within the range" and (2) "the financial reporting context in which the reserve will be presented" (Statement of Principles, p. 13).

Problem S6-7-5.

(a) According to the Statement of Principles (p. 14), what are the five key dates around which the organization of claim data revolves?

(b) On page 14, the Statement of Principles gives both aprecise definition and a broad definition of incurred but not reported (IBNR) claims. State each definition.

(c) Out of what can ambiguity regarding the definition of IBNR arise? (See Statement of Principles, p. 14.)

Solution S6-7-5.

(a) The organization of claim data revolves around the following five key dates:

1. Accident date
2. Report date
3. Recorded date
4. Accounting date
5. Valuation date

(b) Precise definition of IBNR (with respect to a given accounting date): Claims "with report dates later than a particular accounting date and accident dates equal to or earlier than the accounting date" (Statement of Principles, p. 14).

Broad definition of IBNR: Provision for late reported claims, development on known claims, and reopened claims (Statement of Principles, p. 14).

(c) Ambiguity regarding the definition of IBNR can arise from different insurer strategies in loss reserving. The accident period approach and the report period approach are two of the most common strategies. The accident period approach does not necessitate separately treating reported and unreported claims and so lends itself open to the broad definition of IBNR. In the report period approach, claims that have not been reported during a given time period are by definition not a part of the data, and so any IBNR estimate has to be performed separately for such claims.

See other sections of The Actuary's Free Study Guide for Exam 6.