# Claims Reserving Manual

Claims Reserving Manual

(published 1989, updated 1997)

This Manual was prepared and published in the hope that it would help both actuaries and others interested in claims reserving practices. The Manual was created in 1989 and was updated in 1997. While it will contain many relevant principles, we cannot vouch for the appropriateness of any practices suggested in today's rapidly changing world. This will apply particularly to areas that impact reserving in the context of regulation and reporting.

Volume 1 begins with the insurance background, material on the basic purposes of claims reserving, the types of data available, and the internal and external influences which it is important to consider in setting reserves. It then goes on to give an extensive and structured review of the methods available and commonly in use at the present time. There are detailed comments on the assumptions involved, the dependence on the data, and the different approaches available. Volume 1 deals with arithmetic or deterministic methods.

Volume 2 includes more advanced methods involving probabilistic and statistical concepts. The test for the inclusion of a method in Volume 2 was that it had been used by a practitioner with responsibility for advising on the setting of reserves, or commenting on their adequacy, and that he or she found it helpful. The fact that a method may contain weaknesses from a theoretical statistical viewpoint may be commented upon, but did not prevent its publication.

The standpoint of the Manual is that claims reserving is a practical subject which requires informed judgement. The advantage of a method should be that it helps to interpret the data and apply such judgement.

### Volume 1

- Section A: The insurance background
- Section B: Data and forecasting
- Section C: Company and external influences
- Section D: Dimensions of choice
- Section E: The projection of paid claims
- Section F: Case estimates and the projection of incurred claims
- Section G: Methods using loss ratio and loss ratio projections
- Section H: Methods based on claim numbers and average cost per claim
- Section I: Methods for IBNR
- Section J: Dealing with inflation
- Section K: Miscellaneous topics
- Section L: Actuarial considerations
- Section M: Towards a formalised approach
- Section N: Glossary of notation

### Volume 2

- Description of stochastic models
- Papers of more advanced methods
- Precis of other actuarial papers
- Computerised illustration of volume 2 papers

### Volume 1

Section 1: 1997 Update of manual

Section 2: Introduction to reserving

- Description of claims process
- Reserving methodology - general
- Reserving in context
- Commonly used simple reserving methods

Section A: The insurance background

- Purpose of claims reserving
- Types of business - the primary market
- Types of business - reinsurance and the London Market
- Note on technical reserves
- Note on terminology

Section B: Data and forecasting

- The projection of past experience
- Data groupings: principle of homogeneity
- The claims development table
- Data quantities
- Simple breakdowns of the claims pattern
- Data systems and validation
- Forecasting: simple averages and trends
- Mathematical trendlines

Section C: Company and external influences

- Classification and general analysis
- Business mix and volume
- Underwriting, rating and policy conditions
- Claims handling and definition
- Inflation and economic factors
- Legal, political and social factors
- Climate and environmental factors

Section D: Dimensions of choice

- Case reserves v Statistical methods
- Simple statistical methods v Mathematical modelling and stochastic techniques
- All claims together v Separation of large and/or small claims
- Figures gross v Net of reinsurance/claims expense/salvage and subrogation
- Accident (or underwriting) year v Report year cohorts
- Loss ratio v Claim development patterns
- Paid loss v Incurred loss development
- Claim amounts v Use of claim numbers and average cost per claim

Section E: The projection of paid claims

- The grossing up method
- The link ratio method
- Link ratios v grossing up

Section F: Case estimates and the projection of incurred claims

- Nature of case estimates
- The incurred claims function
- Incurred claims - grossing up
- Incurred claims - link ratio method
- Grossing up of case reserves
- Adequacy and consistency of case reserves
- Adjustment of incurred claims projection

Section G: Methods using loss ratio and loss ratio projections

- Concept of loss ratio
- Naive loss ratio method
- Bornhuetter-Ferguson method
- Comparison of results
- Taking stock of the methods
- Sensitivity testing and choice of estimate
- Paid loss ratio - step-by-step projection
- Paid loss ratio and paid claims projection
- Incurred loss ratio and incurred claims projection
- Comparison of results

Section H: Methods based on claim numbers and average cost per claim

- Paid historic claims projection
- Number settled and number reported
- Incurred average claims projection
- Risk exposure and claim frequency
- Correspondence of claim numbers and claim amounts

Section I: Methods for IBNR

- IBNR - definition and ambiguities
- IBNR as the remainder term
- IBNR estimates - the underlying principle
- Alternative bases for IBNR projection
- Tarbell's method and IBNR run-off
- Average cost per IBNR claim
- IBNR by accident year projection
- Adjusted projection using accident and report year

Section J: Dealing with inflation

- Inflation - general considerations
- Inflation adjusted claims projection
- Bennett and Taylor - Method A
- The Separation method

Section K: Miscellaneous topics

- Average cost reserving systems
- Reserves for re-opened claims
- Re-opened claims - Balcarek's method
- Claims expense - indirect type
- Claims expense - direct type

Section L: Actuarial considerations

- The actuarial approach
- The discounting of claims reserves
- Practical example of discounting
- Discounting combined with inflation
- Tracking the performance

Section M: Towards a formalised approach

- The history of a claim
- The claims cohort
- Claim numbers and claim amounts
- Overall loss and the claims reserve
- Primary division of the claims reserve
- The full analysis of loss
- Average cost per claim
- Exposure measures and loss ratio
- Time axes
- Development of claims
- The triangular array
- Claim development and trend analysis

Section N: Glossary of notation

### Volume 2

Section A: Introduction

Section B: Description of stochastic models

Section C: Precis of papers in Section D

Section D: Papers of more advanced methods

Section D1: The chain ladder technique - a stochastic model, by Benjamin Zehnwirth

Section D2: Exponential run-off, by Bjorn Ajne

Section D3: A curve fitting method and a regression method, by Sidney Benjamin and Lawrence M Eagles

Section D4: Reid's method, by D H Reid

Section D5: Regression models based on log-incremental payments, by Stavros Christofides

Accompanying spreadsheet

Section D6: Measuring the variability of chain ladder reserve estimates, by Thomas Mack

Accompanying spreadsheet

Section D7: Probability distribution of outstanding liability from individual payments data, by Thomas S Wright

Section E: Precis of other actuarial papers

- Negative incremental claims: chain ladder and linear models, by Richard J Verrall and Z Li
- A state space representation of the chain ladder linear model, by Richard J Verrall
- Probabilistic development factor models with applications to loss reserve variability, prediction intervals and risk based capital, by Benjamin Zehnwirth
- Stochastic claims reserving when past claim numbers are known, by Thomas S Wright
- Operational time and a fundamental problem of insurance in a data-rich environment, by D H Reid
- Unbiased loss development factors, by Daniel M Murphy
- Using expected loss ratios in reserving, by Daniel F Gogol

Section F: Computerised illustration of volume 2 papers