Estimating Unpaid Claims Using Basic Techniques

By Jacqueline Friedland · Casualty Actuarial Society · 2010

Study guide: Exam 5

A CAS text on estimating unpaid claims for property and casualty insurers, reinsurers and self-insured entities using basic techniques. Written by Jacqueline Friedland of KPMG, with significant contributions by Rachel Dutil and Edward Lam, it was created to replace a number of readings on the CAS's 2007 syllabus with a single educational publication. Its four parts are Introduction, Information Gathering, Basic Techniques for Estimating Unpaid Claims, and Estimating Unpaid Claim Adjustment Expenses; three appendices reproduce a CAS statement of principles and two actuarial standards of practice. This is Version 3, dated July 30, 2010, which added Chapter 17.

On the syllabus

Exam 5 — objectives B1–B20; all chapters (the Appendices are excluded), in the Third Version of July 2010.

Part 1 Introduction

1 Overview

Importance of Accurately Estimating Unpaid Claims
- The importance of accurate estimates of unpaid claims is seen from three viewpoints: internal management, investors and regulators.
Further Requirements for Accurate Reserves
Organization of This Book
Ranges of Unpaid Claim Estimates
- The book focuses on point estimates; addressing ranges of unpaid claim estimates is beyond its scope.
Background Regarding the Examples
Key Terminology
- The unpaid claim estimate has five components — case outstanding on known claims, provision for future development on known claims, estimate for reopened claims, provision for claims incurred but not reported, and provision for claims in transit — and the last four together are the broad definition of IBNR.
- IBNR is often separated into pure IBNR (incurred but not yet reported) and IBNER (incurred but not enough reported, or development on known claims).

2 The Claims Process

Overview
- Claims professionals estimate case outstanding on reported claims; actuaries are responsible for estimating the remaining components of total unpaid claims.
Claims Professionals
A Claim is Reported
The Life of a Claim
Further Claim Examples

Part 2 Information Gathering

Introduction to Part 2 – Information Gathering
- Wiser's four phases — exploring the data, applying estimation techniques, evaluating the conflicting results, and monitoring projections over later calendar periods; Chapters 3 to 6 address the first.

3 Understanding the Types of Data Used in the Estimation of Unpaid Claims

Sources of Data
Homogeneity and Credibility of Data
- The goal is to divide the data into sufficiently homogeneous groupings without compromising its credibility, the predictive value given to a group of data.
Types of Data Used by Actuaries
Organizing the Data
- Key Dates
- Aggregation by Calendar Year
- Aggregation by Accident Year
- Aggregation by Policy Year or Underwriting Year
- Aggregation by Report Year
- Each aggregation — calendar, accident, policy or underwriting, and report year — is set out with its advantages and disadvantages.

4 Meeting with Management

Understanding the Environment
- Reporting and payment patterns, frequency and severity can be altered by changes in classes of business or geographical focus, policy provisions, reinsurance arrangements, claims management philosophy, claims processing lags, the legal and social environment, and the economic environment.
Sample Questions for Department Executives
- Questions for a claims executive, an underwriting executive, a data processing or accounting executive, actuaries specializing in ratemaking, in-house actuaries, those managing reinsurance, and senior management.
Additional Questions

5 The Development Triangle

A development triangle is a table that shows changes in the value of various cohorts over time.
Rows, Diagonals, and Columns
Alternative Format of Development Triangles
Detailed Example of Claim Development Triangles
Other Types of Development Triangles
Naming Convention for Examples

6 The Development Triangle as a Diagnostic Tool

Development triangles are used to see how changes in an insurer's operations and in the external environment — such as in claims settlement and in the adequacy of case outstanding — influence the claims data.
Detailed Example – Background Information
Premium History
The Reported and Paid Claim Triangles
The Ratio of Paid-to-Reported Claims
The Ratio of Paid Claims to On-Level Earned Premium
Claim Count Triangles
Ratio of Closed-to-Reported Claim Counts
Average Claims
Summary Comments for XYZ Insurer
Conclusions

Part 3 Basic Techniques for Estimating Unpaid Claims

Introduction to Part 3 – Basic Techniques for Estimating Unpaid Claims
- The Components of Ultimate Claims
  - Ultimate claims are the sum of cumulative paid claims, case outstanding and IBNR, in proportions that differ between short-tail and long-tail lines.
- Actuarial Judgment

7 Development Technique

The development technique, also known as the chain ladder technique, assumes that claims recorded to date will continue to develop in a similar manner in the future.
Key Assumptions
Common Uses of the Development Technique
Mechanics of the Development Technique
- Seven steps: compile claims data in a development triangle, calculate age-to-age factors, calculate their averages, select claim development factors, select a tail factor, calculate cumulative claim development factors, and project ultimate claims.
Unpaid Claim Estimate Based on the Development Technique
Reporting and Payment Patterns
Observations and Common Relationships
When the Development Technique Works and When it Does Not
XYZ Insurer
Influence of a Changing Environment on the Claim Development Technique

8 Expected Claims Technique

The expected claims technique assumes the actuary can better estimate total unpaid claims from an a priori estimate than from the claims experience observed to date.
Key Assumption
Common Uses of the Expected Claims Method
Mechanics of the Expected Claims Technique
XYZ Insurer
When the Expected Claims Technique Works and When it Does Not
Influence of a Changing Environment on the Expected Claims Technique

9 Bornhuetter-Ferguson Technique

The Bornhuetter-Ferguson technique splits ultimate claims into actual reported (or paid) claims and expected unreported (or unpaid) claims; as a credibility weighting of the development and expected claims methods, Z = 1.00 / cumulative development factor.
Key Assumptions
Common Uses of the Bornhuetter-Ferguson Technique
Mechanics of the Bornhuetter-Ferguson Technique
Unpaid Claim Estimate Based on Bornhuetter-Ferguson Technique
When the Bornhuetter-Ferguson Technique Works and When it Does Not
The Bornhuetter-Ferguson Method and Cumulative CDFs Less than 1.00
XYZ Insurer
Influence of a Changing Environment on the Bornhuetter-Ferguson Method
Benktander Technique
- The Benktander method is a credibility-weighted average of the Bornhuetter-Ferguson technique and the development technique.

10 Cape Cod Technique

The Cape Cod (Stanard-Buhlmann) method obtains the expected claim ratio from the reported claims experience, with "used-up premium" as its denominator, instead of an independent, often judgmental selection.
Key Assumptions
Common Uses of the Cape Cod Technique
Mechanics of the Cape Cod Technique
Unpaid Claim Estimate Based on Cape Cod Technique
When the Cape Cod Technique Works and When it Does Not
XYZ Insurer
Influence of a Changing Environment on the Cape Cod Method

11 Frequency-Severity Techniques

In their simplest form, frequency-severity techniques multiply the estimated ultimate number of claims by the estimated ultimate average value.
Common Uses of Frequency-Severity Techniques
Types of Frequency-Severity Techniques
Frequency-Severity Approach #1 – Development Technique with Claim Counts and Severities
Frequency-Severity Approach #2 – Incorporation of Exposures and Inflation into the Methodology
Frequency-Severity Approach #3 – Disposal Rate Technique
When the Frequency-Severity Techniques Work and When they Do Not
Enhancements for Frequency-Severity Techniques
Frequency-Severity Projection as Input to Bornhuetter-Ferguson Technique

12 Case Outstanding Development Technique

The case outstanding development technique assumes that claims activity related to IBNR is related consistently to claims already reported, so it suits lines whose claims are mostly reported in the first accident period — which makes it strong for claims-made coverages and report year analysis.
Case Outstanding Development Technique – Approach #1
Case Outstanding Development Technique – Approach #2

13 Berquist-Sherman Techniques

Reacting to a Changing Environment through Data Selection and Rearrangement
Treat Problem Areas through Data Adjustment
- Detecting Changes in the Adequacy Level of Case Outstanding and Reducing the Effect of Such Changes on Reported Claims Projections
- Detecting Changes in the Rate of Settlement of Claims and Adjusting Paid Claims for Such Changes
- The Berquist-Sherman adjustments restate the case outstanding triangle for changes in case outstanding adequacy, and the paid claim triangle for changes in the rate of claims settlement, before development techniques are applied.
XYZ Insurer

14 Recoveries: Salvage and Subrogation and Reinsurance

Salvage, Subrogation, and Collateral Sources
Estimating S&S Recoveries – Auto Physical Damage Insurer
- Salvage and Subrogation recoveries are projected with the development technique on reported and received S&S, and with a ratio approach developing the ratio of received S&S to paid claims.
Reinsurance and Aggregate Limits
- All the techniques of Chapters 7 to 13 can be applied to gross, ceded or net of reinsurance claims experience.

15 Evaluation of Techniques

Actuaries should use more than one method when analyzing unpaid claims; no single method can produce the best estimate in all situations.
U.S. Industry Auto
XYZ Insurer
Changing Conditions – Changes in Claim Ratios and Case Outstanding Adequacy and Changes in Product Mix
Berq-Sher Insurers
Monitoring and Interim Techniques for Unpaid Claim Estimates
- Comparisons of actual and expected claims, and roll-forward analyses between complete, detailed analyses.

Part 4 Estimating Unpaid Claim Adjustment Expenses

Introduction to Part 4 – Estimating Unpaid Claim Adjustment Expenses
- Actuaries in Canada still separate ALAE and ULAE; for U.S. Schedule P reporting the NAIC introduced defense and cost containment (DCC) and adjusting and other (A&O) expenses, effective January 1, 1998.

16 Estimating Unpaid Allocated Claim Adjustment Expenses

All the development techniques of Part 3 can be used with ALAE; the greatest challenge is often obtaining ALAE data separate from claim-only data.
Example – Auto Property Damage Insurer
- Reported and paid ALAE development, the development of the ratio of paid ALAE to paid claims, and that ratio with additive rather than multiplicative development factors.
Choosing a Technique for Estimating Unpaid ALAE

17 Estimating Unpaid Unallocated Claim Adjustment Expenses

The two broad classifications of techniques for ULAE are dollar-based and count-based; the chapter relies extensively on Conger and Nolibos (2003), "Estimating ULAE Liabilities: Rediscovering and Expanding Kittel's Approach".
Dollar-Based Techniques
- Classical (or Traditional) Technique
- Kittel Refinement
- Conger and Nolibos Method – Generalized Kittel Approach
- Mango-Allen Refinement
Count-Based Techniques
- Early Count Techniques
- Wendy Johnson Technique
- Mango-Allen Claim Staffing Technique
- Rahardjo
- Spalla
Triangle-Based Techniques
Comparison Example

Appendices – Statement of Principles and Actuarial Standards of Practice

Appendix A Statement of Principles Regarding Property and Casualty Loss and Loss Adjustment Expense Reserves

Appendix B Actuarial Standard of Practice No. 43 Property/Casualty Unpaid Claim Estimates

Appendix C Actuarial Standard of Practice No. 9 Documentation and Disclosure in Property and Casualty Insurance Ratemaking, Loss Reserving, and Valuations

List of Changes Implemented

July 30, 2010: Chapter 17 added, and the page number for Chapter 11 corrected in the table of contents.
July 22, 2009: hyperlinks and bookmarks added, "affect" changed to "effect" where appropriate, and corrections to exhibits in Chapters 13, 14 and 15.

Errata

Chapter 17, page 388, under "Challenges of the Classical Technique": the 25% and 75% ratios apply to opening and closing claims, implying 75% of the ULAE ratio applied to case outstanding and 100% to IBNR.

Sources

Estimating Unpaid Claims Using Basic Techniques (Casualty Actuarial Society, 2010) — the document (Version 3, July 30, 2010): title page, acknowledgments, table of contents and bookmarks, each chapter's section headings, the chapter text the points above are taken from, the list of changes and the errata page
CAS Exam 5 Content Outline, Fall 2026 — the citation and the assigned scope