Machine Learning and Traditional Methods Synergy in Non-Life Reserving

131 Pages·2017·1.98 MB·English

Machine Learning
and Traditional
Methods Synergy in
Non-Life Reserving
2018 REPORT
Machine Learning and Traditional Methods Synergy in Non-Life
Reserving (MLTMS)
ASTIN WORKING PARTY | 2017/2018
Machine Learning & Traditional Methods Synergy in Non-Life reserving
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ASTIN 2018 Working Party
Authors of the report
Salma Jamal (Head of the project)
Stefano Canto
Ross Fernwood
Claudio Giancaterino
Munir Hiabu
Lorenzo Invernizzi
Tetiana Korzhynska
Zachary Martin
Hong Shen
Other members
Brij Bhushan Sharma Shane O’Dea
Alan Chalk Francesco Pio Mesiano
Rocco Cerchiara Peng Shi
Francesco Cuzzucrea Benjamin Smith
Miyuki Ebisaki Hidemasa Oda
Tobias Heinrich Michael Radtke
Yuji Hiramatsu Greg Taylor
Christoph Krischanitz Gary Venter
Kevin Kuo Gary Wang
Vittorio Magatti Radost Wenman
Lawrence McTaggart Marcel Wiedemann
Jacqueline Micheller Sabrina Zhang
Peter Mulquiney
Acknowledgment
We would like to express our thanks to Greg Taylor for helpful contribution and insightful
discussions and suggestions that significantly improved this paper.
The authors would also like to expressly thank Frank Cuypers and Emiliano Valdez for
supporting the initiative of this Working Party.
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Contents
1. Abstract 3
2. Introduction 4
3. Structure of the study 5
4. Swiss Re Data 7
4.1. Data presentation 7
4.2. Data processing 8
4.2.1. Initial Processing 8
4.2.2. Data Sets for loss reserving models 10
4.2.3. Exploratory Data Analysis 11
5. Loss reserves Modelling 12
5.1. Modelling with Traditional Methods 13
5.1.1. Preamble 13
5.1.2. The chain ladder 14
5.1.3. Generalized Linear Models 19
5.2. Modelling with Machine Learning 27
5.2.1. Preamble 27
5.2.2. Random forests 33
5.2.3. Neural Networks 38
5.2.4. Gradient Boosting Machine (GBM) 42
5.2.5. Gradient Boosting Machine (GBM) Combined 46
5.2.6. Boosted Tweedie Compound Poisson Model (TDboost) 47
5.2.7. Pure IBNR Estimation 50
6. Comparison and evaluation of models 53
6.1. General strategy 53
6.2. Yearly Cash Flows 54
6.3. Total Outstanding 55
6.4. Individual Cell Errors 56
7. Conclusion 58
7.1. Step back on the study 58
7.2. Synergy between Machine Learning and traditional methods 61
7.3. Advantages and drawbacks of traditional methods and Machine Learning techniques
62
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7.4. Clues for future works 64
8. References 66
9. Appendices 68
9.1. Exploratory Data Analysis 68
9.1.1. Further analysis 69
9.2. Triangles of claim experience 70
9.3. Summary of results 71
9.3.1. Ultimates 71
9.3.2. Loss Reserves 77
9.4. Results by Method 83
9.4.1. Forecasts based on Traditional Methods 83
9.4.1.2. Generalized Linear Models 98
9.4.2. Forecasts based on Machine Learning Methods 102
9.5. Models validation and comparison for reserving 128
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1. Abstract
Actuaries are well acquainted with traditional reserving methods such as chain ladder and
Bornhuetter-Ferguson. These traditional actuarial methods have been shown over many
decades of actuarial practice, and in certain circumstances, to work well at an aggregate level
to calculate appropriate reserve provisions. However, today with improvements in analytical
methods and technology, actuaries are better equipped to uncover detailed loss drivers using
Machine Learning techniques. Nowadays, insurers are highly interested in the anatomy of their
portfolios. From claimants’ behaviours, business strategies or portfolio pruning, sources of data
volatility are numerous and impact both the reserving and the pricing processes of an insurer.
Machine Learning methods can identify obscure trends in the data and incorporate suitable
adjustments in its forecasts. When used together, traditional methods and Machine Learning
methods can both support reserve estimates as well as provide the business explanations that
are demanded by our stakeholders. The aim of our working group is to demonstrate that their
joint application can be a powerful decision-making tool.
Our study focused on a real data set provided by Swiss Re. The Line of Business concerned is
Professional Liability. After a processing phase, traditional methods such as chain ladder and
GLM have been compared to a range of five Machine Learning methods. A synthesis completes
the study, highlighting its limits and suggesting avenues of reflection for future research.
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2. Introduction
As long as insurance has existed, the need for calculating reserves has existed. Traditionally,
Non-Life insurers apply triangulation techniques to aggregated claims data by accident year and
development year. The challenge of loss reserving involves making predictions about how
claims costs will emerge in the future based on an analysis of past claims data and our
expectations about the future. Claims data can be noisy and changeable and a key difficulty
can be understanding those changes in the presence of noise.
Traditional methods in loss reserving usually possess two features: i) they are based on a
statistical model whose algebraic form is very simple, e.g. that the expected amount of paid
claims in a cell is equal to the simple product of an accident year factor and a development year
factor; and ii) they are calibrated by elementary arithmetic procedures, such as averaging over
rows and/or columns.
It is common that real-life claim data do not conform neatly with the first characteristic. The
true underlying model may be much more complex. Its form may be unknown. Even if it is
known, adaptation of the elementary calibration procedures described becomes cumbersome
or fails completely.
Machine Learning methods are one option for addressing this situation. They offer a
sophisticated and efficient tool for understanding and modelling past claims characteristics.
They allow one to discard the simplistic underlying assumptions about data structure implied
by traditional reserving models and so provide the ability to build more accurate models.
The application of these two families of methods relies on a specific methodological scheme
for each of them. For the traditional methods, the challenge is to integrate in the development
factors the particularities of the data (for example, a volatile volumetry of claims by
development year). For Machine Learning methods, insofar as a parameters optimization
algorithm is introduced to control the risk of over-learning, the challenge behind their use was
the upstream choice of the explanatory variables and the understanding of the interest of the
parameters of each model.
Machine Learning methods are powerful in the recognition of very fine patterns in data but
they cannot, at least not so far, supplant traditional methods. The ambition of this working
group is to demonstrate that Machine Learning methods, as well as traditional methods each
have their own strengths. We illustrate this by the complementary conclusions that their
application to real data leads to.
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3. Structure of the study
This medium presents the study on the synergy between traditional methods and Machine
Learning techniques for Non-Life reserving. The detailed results are presented in the
appendices at the end of the report.
This study has been structured as following:
1. Data processing
In this section, the data set used for the study is presented. The main processing
operations applied to prepare the data for the modelling step are developed;
2. Loss reserves modelling
i. Application of traditional methods :
In this section, traditional methods such as chain ladder and Generalized Linear
Models are applied to the data set.
Their respective application responds to the general academic framework but
relies also on expert judgment, especially for tail extrapolation needs.
ii. Application of Machine Learning methods
In this section, Machine Learning methods are applied to the data set.
These models do not use a triangular data structure. The modelling dataset use
both transactional detail and information about the policies and the claimants.
The modelling separates the projection of Incurred But Not Enough Reported
(IBNER) from Incurred by not Yet Reported (IBNYR or pure IBNR):
 IBNER projection is based on the two component models:
 The first model estimates the incremental paid/incurred amounts
conditional upon a claim being open at the beginning of the period. A
variety of different Machine Learning models could be employed here
such as Gradient Boosting Machine, Neural Networks, Random Forest,
etc.
 The second model estimates the propensity of a claim to be open at a
particular point in time (again we can choose from a variety of
Machine Learning methods). From this second model, appropriate
conditional probabilities can be calculated to be applied against model
1. Therefore, an estimate of incremental transaction amounts can be
made by “blending” these two model results together.
Remark: One should note that there is a claim-specific connection
between these two models as both models are modeled at the same level
of granularity (e.g. claim or claimant).
 IBNYR projection is based on a frequency severity approach. Frequency
model predicts the future newly reported claim counts at a given
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development year, then the severity model provides the average severity
for these claims reported at that development year.
 For frequency, the number of expected reported claims is estimated
at each future time period. The frequency model is based on
aggregated data. The target here is the reported ratio. The model will
then predict the reported ratio at future development years to derive
the future newly reported claims;
 For severity, the results from the IBNER model are utilized as an input
into the severity model. This model is at a claim level. The target here
is ultimate severity.
Predictors of this model have to be the same variables as the
frequency model.
The product of the two models gives a pure IBNR estimate.
One key variable for this approach is the development year when the claim was
reported: it is the one used to combine the severity model with frequency model.
This approach is in some extent a simplified one since there is no significant
history of IBNR claims in the data set of this study.
3. Comparison of models
The results of the various models are compared with different indicators: yearly cash
flows, total outstanding and individual cell errors.
4. Findings on the synergy between traditional methods and Machine Learning for Non-
Life reserving
The conclusion of the report consists of taking a step back on the contribution of each
model to Non-Life reserving in both the case of the data set of this study and on a macro
level. Clues for improvement are also identified at the end of the report.
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4. Swiss Re Data
4.1. Data presentation
4.1.1.1. Data set
The Line of Business for this portfolio is Professional Liability, covering “Claims made”.
It is, at least in this study, characterized by:
 Long and heavy tail ;
 Claims covers experience from 1994 to 2016 inclusive ;
 Different behavior related to the profession of claimants ;
 Significant deferment between accident year and reporting year (between 3 and 5 years
in average). An analysis of claims deferment is presented in Appendix 9.1.1.1. Claims
deferment;
 Volatility of the claims development at an individual level ;
 Calendar year effects like inflation, legal changes
4.1.1.2. Variables
The dataset was initially composed of 16 variables, of which we selected those presented in
Table 1.
Variable Type Descritpion
Paid YY Numerical Payment of the year YY (incremental)
O/S YY Numerical Case reserve (outstanding) of the year YY (cumulative)
Incurred YY Numerical Incurred amount of the year YY (incremental)
UWY Discrete Underwriting year
DoL Discrete Accident year (Date of Loss)
DoN Discrete Reporting year (Date of Notification)
Settlement Year Discrete Settlement year for claims that are already closed
Year of Birth Discrete Birth date of the claimant
Insured Categorical Anonymized code of insured entity
Loss Number Categorical Univocal number of claim
Open / Close Categorical Status of claim (1 for open and 2 for close)
Age Group Categorical Grouping claimants in age classes
Insured Profession Categorical Groups of claimants' profession
Incident Grouping Categorical Subcategory related to Insured field
Case specialty Categorical Description of Claim Event
Event Categorical Flag for difficult type of losses (expensive and long-tail claims)
Table 1 Main variables of the study
On the one hand, the data set can be converted into aggregate triangles by accident year and
development year, which correspond to the appropriate format to build a classic method to
estimate the claims reserve.
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On the other hand, the other variables selected are used as explanatory variables in the
Machine Learning models.
4.2. Data processing
Data was provided by the reinsurer in the form of a flat text file, detailing insurance losses on a
claim level evaluated at various points in time, and some categorical features of the claimant.
Broadly, there were three goals in processing the data:
Step Purpose Description
Understanding and potentially correcting data issues that may
Initial
1 undermine either traditional reserving analyses or Machine
Processing
Learning methods
The form of these data sets depends on their intended use:
- For traditional reserving methods, traditional paid and
Data Sets for
incurred loss triangles are needed.
2 loss reserving
- For Machine Learning methods, target variables and
models
potential features are needed, as well as a further split of
between training and test sets .
Exploratory Gaining initial understanding of high level trends and patterns that
3
Data Analysis may inform further analysis
Table 2 Data processing steps
These three steps are described below in more detail.
4.2.1. Initial Processing
This section can be further divided into three parts:
 Exception handling/data issues
 Reformatting
 Derivation of additional fields.
4.2.1.1. Exception handling and data issues
In the process of data collection, inconsistencies have been identified on some individual
entries. Example of these inconsistencies is that for some claims the date of their reporting was
prior to the one of the accident year (reporting year < accident year).
The results of the processing are presented in Table 3.
One should note that the increasing amounts of claims after processing are due to the removal
of negative claims.
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