San Francisco - Data Mining Techniques in Actuarial Modeling

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Data Mining Techniques & Its Applications in Insurance

Society of ActuariesSan Francisco Spring Meeting

June 24 - 26, 2002

Lijia Guo, PhD, ASA, MAAAUniversity of Central Florida

Session 11L

SOA San Francisco Spring MeetingJune 24-26, 2002

Slide 2

Learning Objectives

§ Understanding a Data Mining Process§ Having insight about the actuarial

applications of data mining techniques § Exploring the perspective of applying data

mining techniques in your own practice

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Slide 3

Agenda

§ Introduction§ Data Mining Methods§ Actuarial Applications§ Conclusions & Questions


Slide 4

Introduction

§ Changes in Information Technology § Availability of large quantity of insurance

data§ Mind your business by mining your data

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Slide 5

What is Data Mining?

§ An information discovery process.• Prediction

-- Finding unknown values/relationships/patterns from known large database

• Description-- interpretation of a large database

§ Making crucial business decisions - turn the newfound knowledge into actionable results


Slide 6

Why Use Data Mining?

§ Product development§ Marketing§ Analysis of Claims Distribution§ Healthcare§ ALM§ Fraud detection§ Solvency analysis

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Slide 7

Data Mining Methods

§ Classification§ Regression§ Clustering§ Summarizations§ Dependency modeling§ Deviation Detection


Slide 8

Data Mining Algorithms

§ Decision Trees (Breiman et al., 1984)§ Logistic regression (Hosmer & Lemeshow,

1989) § Neural Networks (Bishop, 1995; Ripley, 1996) § Fuzzy Logics§ Genetic Algorithms (Goldberg, 1989)§ Bayesian analysis, (Cheeseman et al., 1988)§ Hybrid algorithms

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Slide 9

Data Mining Algorithms-- Decision Trees

§ What are decision trees§ How decision trees work

• Choosing variables• Grouping• Creating the leaf nodes of the tree

§ Strengths and weaknesses


Slide 10

Data Mining Algorithms-- Neural Networks

§ What are Neural Networks§ How Neural Networks work

• Processing elements• Training• Predicting

§ Strengths and weaknesses

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Slide 11

Data Mining Algorithms-- Hybrid Algorithms

§ Problems with standard algorithms§ Advanced algorithms§ Discovery-driven approaches§ Mixture of algorithms


Slide 12

Data Mining: Knowledge Discovery Process

§ Data Acquisition§ Data integration§ Data exploration § Model building§ Understanding your model§ Post-mining analysis

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Slide 13

Data Mining Process: Data Acquisition

§ Data acquisition• Getting your data• Data qualification issues• Data quality issues• Data derivation

§ Defining a study• Basic Risk Characteristics


Slide 14

Data Mining Process:Data Acquisition -- Case Study

§ SOA database for RP-2000 Mortality Tables• 10,957,103 exposed life-years

§ Subset of the database that includes all the lives above age 70 (3,769,956 exp, 217,490 death)§ Risk groups

• Age, gender, participation status, union, pay type, collar type, and annuity amount, etc.

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Slide 15

Data Mining Process:Data Acquisition -- Case Study

§ Existing study on advanced-age mortality• Smooth extension of the patterns • Families of curves - Gompertz law, etc.• All these approaches aim at explaining the age

pattern of mortality.

§ Mortality distribution varies among seniors with different backgrounds


Slide 16

Data Mining Process: Data Integration

§ To identify the factors that influence mortality§ To study the interaction of the risk factors§ To gain the perspective on the importance

of these factors

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Slide 17


Slide 18

Data Mining Process: Data Integration-- Case Study

§ Main effect exists for all six variables considered§ Degrees of the effects of the risk factors are

different.• the interaction of these factors • the importance of the factors

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Slide 19

Data Mining Process: Data exploration

§ Decision tree algorithm • Analyze the influences and the importance of

the mortality risk factors • observations are grouped into several segments

§ Algorithm - SAS/Enterprise Miner Version 4.2 (2001).§ Further study the interaction and the

importance of the risk factors


Slide 20

Data Mining Process: Data Integration-- Case Study

§ Variable Importance MeasureVariable Importance

Participation Status 1.00

Gender 0.75

Annuity size 0.43

Pay Type 0.21

Union 0.18

Collar 0.00

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Slide 22


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Slide 23

§ Six risk groups: • Employees• Beneficiaries• Combined• Disabled• Male Retirees• Female Retirees.

§ Logistic regression method

Data Mining Process: Model building


Slide 24

Data Mining Process: Model Building --Case Study: Female “Retiree”

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Slide 25

Data Mining Process: Model Building-- Case Study: Female “Retiree” Group

§ “Collar” and “Pay Type” are two important variables§ The interaction between “Collar” and “Pay

Type” does exist§ Both “annuity size” and “union” are not

picked up by tree algorithm


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Data Mining Process: Model Building-- Case Study: Female “Retiree” Group

§ R-square for the regression is 0.95

PTCPTCxxp

p046.000087.026.097.17

1log 2 −+−−+−=

−

=

collarmixed

collarbluecollarwhite

C

0047.0

00

=

typepaysalarizedtypepayhourly

typepaycombinedPT

0051.0033.0

Where p is the mortality rate, x is the age

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Slide 27

Data Mining Process: Model Building -- Case Study: Female “Retiree” Group


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Data Mining Process: Model Building-- Case Study: Male “Retiree” Group

§ R-square for the regression is 0.92

Where p is the mortality rate, x is the age

SUUSxxp

p +−−−+−=

−

200055.020.057.141

log

=

annuitysmallannuitymedian

annuityel

S0074.0060.0

arg044.0

−=combined

memberunionnonmemberunion

U

040.0

14.00

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Slide 29

Data Mining Process: SEMMA


Slide 30

Data Mining Process: Model Building -- Case Study: Male“Retiree”

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Slide 31

Data Mining Process: Post-mining Analysis -- Case Study


Slide 32

Data Mining Process: Understanding your model – Case Study

§ The male retirees mortality model and the female retirees mortality model depend on different variables§ Mortality of the beneficiaries is determined by

gender, annuity size, the pay type, and their interactions § The gender factors will play a much-reduced role

in determining beneficiaries’ mortality model

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Slide 33

Data Mining Process: Post-mining Analysis -- Case Study

§ Limited results on the mortality distribution for the ages above 95 § As the female demography changed in the past

three decade, variables such as annuity size, and union will play more important role in determining the female mortality§ Other risk factors such as education, life style,

smoking/non-smoking, etc.


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Data Mining Process: Summary-- Case Study

§ Non Gompertz (linear growth) between age 70 and 85§ Selection of the risk factors may influence

the quality of the mortality model§ Mortality models varies with the most

important risk factor (the participating status, in this study) among all the other variables

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Slide 35

Data Mining Process: -- Case Study in Claim Analysis

§ Basic risk characteristics§ Top-down identification§ Underlying statistical properties§ Domain-specific constraints


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Data Mining Process: -- Case Study in ALM

§ Decision tree and DNF learning

§ Generative stochastic modeling• Probabilistic networks• Probabilistic Rules

§ Hidden Markov model

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Slide 37

Data Mining Process: -- Applications in Healthcare

§ More productive managed care program§ Pricing § Individual health insurance market§ Recovery & prevention of fraudulent claims§ Prescription Drugs cost management


Slide 38

Quiz on Data mining

§ What is Data Mining?§ What can data mining do?§ What are data mining techniques?§ What are the applications of data mining?§ How can you practice on data mining?

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Slide 39

Summary

§ Overview of data mining techniques§ Its application to actuarial practice§ Future developments§ Potential contribution to your area

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San Francisco - Data Mining Techniques in Actuarial Modeling