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ReservePrism
Predictive Modeling for Insurers
Kailan Shang CFA, FSA, PRM, SCJPVice President, Predictive Modeling, Reserve Prism
Managing Director, Swin Solutions
November 2016
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Agenda
• What is Predictive Modeling?
• Predictive Models
• Insurance Applications
• Case Studies
UBI/Telematics
Insurance Product Recommendation
Underwriting
Crime Classification
• Demo
Predictive Modeling
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What is Predictive Modeling?
• The process of using statistical models to predict future trends and behaviors.
• Synonyms: Statistical modeling, regression analysis, data mining, machine learning, data science, etc.
• In the actuarial world, the most widely used predictive model is Generalized Linear Model (GLM).
• But there are a lot more to explore ……
Predictive Modeling
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ReservePrismPredictive Modeling Process
Data
Collection
Data
Processing
Model
Fitting
Model
Testing
Data
Visualization
Structured Data (Numerical)
Unstructured Data (Text, Voice, Image)
Feature Extraction
Missing Data Treatment
Principal Component Analysis
Data Normalization
Categorical Dummy
Classification
Regression
Training Data/ Validation Data
Precision (Type I) /Recall (Type II)
Result Communication
Linkage to Decision-Making
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Clustering Analysis: k-means, distribution based clustering, etc.
Principal Component Analysis: Less variables to explain most of the volatility in the data
Unsupervised Learning: We do not know Y
Predictive Models
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Association Rules: Item Sets
Beer + Diaper
Unsupervised Learning: We do not know Y
Predictive Models
Base Policy
+ Rider?
+ Options?
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Linear Regression: Y = a + bX + ϵ
Generalized Linear Model (GLM): Assuming something different from normal distribution.
•Probability distribution from the exponential family. (Binomial for Logistic distribution)
•Linear predictor η = Xβ.
•Link function g such that E(Y) = μ = g−1(η). (Xb=ln(m/(1-m)) for
logistic regression)
•A lot of distribution to choose: Exponential, Gamma, Inverse Guassian, Poisson, Multinomial, etc.
Supervised Learning: We know Y
Predictive Models
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Decision Tree
Supervised Learning: We know Y
Predictive Models
Income
<92.5 >=92.5
High Risk
Dwelling
Status
No Yes
EducationLow Risk
High Low
Low Risk High Risk
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Classification and Regression Tree (CART)
Supervised Learning: We know Y
Predictive Models
X3 <10
X7 <36.7
X5 <2.67
X9 <10.75
X12 <599.4
Y = 4.2; N = 56
Y = 3.7 ; N = 336
Y = 0 ; N = 235
Y = 21 ; N = 15
Y = 1.6 ; N = 126Y = 0 ; N = 20
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Random Forest: random version of CART
Supervised Learning: We know Y
Predictive Models
CARTsPredicted
ResultVote
Y = 0
Y1 ~ X1
Y = 0 (23)
Y2 ~ X2 Y = 1 Y = 1 (177)
Sampling
Y3 ~ X3 Y = 1 Y= 1
Yn ~ Xn Y = 1
Training
Data
Y ~ X
… … …
X3 <10
X7 <36.7
X5 <2.67
X9 <10.75
X12 <599.4
Y = 1 (5/67)
Y = 0 (15/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (2/13)Y = 0 (5/1)
X3 <10
X7 <36.7
X5 <2.67
X9 <10.75
X12 <599.4
Y = 1 (5/67)
Y = 0 (15/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (2/13)Y = 0 (5/1)
X4 <20
X12 <599.4
X9 <10.75
X12 <599.4
Y = 1 (6/67)
Y = 0 (12/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (1/4)
X4 <20
X6 <6.7
X5 <2.67
X9 <10.75
X12 <599.4
Y = 1 (6/67)
Y = 0 (12/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (2/13)Y = 0 (5/1)
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Artificial Neural Network (Deep Learning)
Supervised Learning: We know Y
Predictive Models
X1
...
X3
X2
a1
a2
a3
a4
b1
b2
bn-1
bn
Y1
Y1
Input OutputLayers
X1
...
X3
X2
a1
a2
a3
a4
b1
b2
bn-1
bn
Y1
Input OutputLayers
X1
...
X3
X2
a1
a2
a3
a4
b1
b2
bn-1
bn
Y2
Input OutputLayersInput OutputLayers
X1
...
X3
X2
a1
a2
a3
a4
b1
b2
bn-1
bn
Input OutputHidden Layers
ai=f (x1,x2,x3) bi=g (a1,...,a4) Yi=h (b1,...,bn)
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Bayesian Network
Supervised Learning: We know Y
Predictive Models
Product Complexity
Penalty CostMisunderstandingCompensation
Level
Misleading Advertisement
A
B D
E
1
34
5
2
P (Complex) = 0.3
P (High|Complex) = 0.8P (Low|Complex) = 0.2
P (High) = 0.5
P (High|Complex) = 0.65P (Low|Complex) = 0.35 P (High|High B & High C & High
D) = 0.95P (Low|High B & High C & High
D) = 0.05... ...
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Hidden Markov Model
Supervised Learning: We know Y
Predictive Models
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ReservePrismInsurance Application
PricingMore pricing factors
ReservingClaim classificationCase reserve adequacy assessmentFalse claim identificationClaim closure/reopenessClaim size prediction
UnderwritingHigh risk case identificationAutomatic underwriting
MarketingCustomer retention, renew, or resellPersonalized product recommendationCustomer categorization
Risk AnalysisFraud detectionCredit score
Business DisruptionUBIHealth/Fitness discount
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ReservePrismCase Study: UBI/Telematics
X y
0 0
-7.4 -7.5
-15 -14.8
-22.6 -22.1
-29.9 -28.9
-37.7 -35.3
-44.7 -42.3
-51.5 -49.6
… …
One second later, the vehicle moved to (-7.4, -7.5), which is 7.4m south and 7.5m west of the starting point.
Each driver has 200 driving paths
Raw Geolocation Data
The paper can be downloaded at
http://reserveprism.com/docs/PredictiveModelingUsingTelematics.pdf
Its Chinese version has been published by the CAA
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ReservePrismCase Study: UBI/Telematics
Feature Extraction (Pricing/ Risk Assessment)
Feature Explanation
Time The time of a trip, by counting the number of rows in a trip file.
Speedavg Average speed
Speedvol Standard deviation of the speed
Speedmin Minimum speed
Speedmax Maximum speed
Speed10 10th percentile of speed
Speed30 30th percentile of speed
Speed70 70th percentile of speed
Speed90 90th percentile of speed
accelerationavg Average acceleration
accelerationvol Standard deviation of the acceleration
accelerationmin Minimum acceleration
accelerationmax Maximum acceleration
Acceleration10 10th percentile of acceleration
Acceleration30 30th percentile of acceleration
Acceleration70 70th percentile of acceleration
Acceleration90 90th percentile of acceleration
Nofast Number of accelerations greater than 2
Noslow Number of decelerations less than -2
segdistanceavg Average distance per second
segdistancevol Standard deviation of the distance
Length Length of the trip (average speed * time)
Indicator (Y) Whether the trip belongs to the driver. At initial, it is assumed that the 200 trips in a driver’s folder
all belong to the driver.
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ReservePrismCase Study: UBI/Telematics
We want to predict if a certain driving trip was driven by the policyholder.
Unsupervised Supervised
Driver 1:Training
Data (700 Trips)
Driver 1: 200
Driving Trips
Driver 2: 200
Driving Trips
Driver 2:Training
Data (700 Trips)
Driver N: 200
Driving Trips
Driver 3:Training
Data (700 Trips)
…
200 Trips
500 Random Trips
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ReservePrismCase Study: UBI/Telematics
Random Forest
CARTsPredicted
ResultVote
Y = 0
Y1 ~ X1
Y = 0 (23)
Y2 ~ X2 Y = 1 Y = 1 (177)
Sampling
Y3 ~ X3 Y = 1 Y= 1
Yn ~ Xn Y = 1
Training
Data
Y ~ X
… … …
X3 <10
X7 <36.7
X5 <2.67
X9 <10.75
X12 <599.4
Y = 1 (5/67)
Y = 0 (15/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (2/13)Y = 0 (5/1)
X3 <10
X7 <36.7
X5 <2.67
X9 <10.75
X12 <599.4
Y = 1 (5/67)
Y = 0 (15/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (2/13)Y = 0 (5/1)
X4 <20
X12 <599.4
X9 <10.75
X12 <599.4
Y = 1 (6/67)
Y = 0 (12/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (1/4)
X4 <20
X6 <6.7
X5 <2.67
X9 <10.75
X12 <599.4
Y = 1 (6/67)
Y = 0 (12/1)
Y = 0 (6/1)
Y = 1 (1/4)
Y = 1 (2/13)Y = 0 (5/1)
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ReservePrismCase Study: UBI/Telematics
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ReservePrismCase Study: UBI/Telematics
Validation
Confusion Matrix
Total Trips Predicted Right Trips Predicted Wrong Trips
Actual Right Trips True Right Trips False Wrong Trips
Actual Wrong Trips False Right Trips True Wrong Trips
Total Trips Predicted Right Trips Predicted Wrong Trips
Actual Right Trips 43 7
Actual Wrong Trips 15 185
A more mature business model with time and actual coordinates.
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ReservePrismCase Study: Insurance Product Recommendation
Data
Demographic
Information
Financial
information
Purchase
History
Claim
History
Communication
history
age, gender, address, zip code,
smoker/nonsmoker, health status,
occupation, marital status
assets, real estate, income,
loans and spending
product type, product name, issue
age, face amount, premium rate, face
amount change, partial withdrawal,
policy loan and product conversion
time, amount, payment
last contact time, reason,
outcome, complaints
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ReservePrismCase Study: Insurance Product Recommendation
Data Processing
1. Non-numerical data Grouping and Converting to dummy
variable
2. Missing data Use the value of the similar records.
• Similarity is measured by the Euclidean distance.
where
X is the data record with missing value for variable l
Y is a complete data record in the dataset.
n is the number of variables in the dataset.
𝑌𝑖 − 𝑋𝑖 2
𝑛
𝑖=1
𝑖 ≠ 𝑙
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ReservePrismCase Study: Insurance Product Recommendation
Model: Artificial Neural Network
Input
Datag (1) Hidden
Layerg (2) Hidden
Layerg (3) Output
The essay is published by the SOA
https://www.soa.org/Files/Research/research-
2016-predictive-analytics-call-essays.pdf
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ReservePrismCase Study: Insurance Product Recommendation
Heuristic Training
Affordability
Satisfaction
Demographic
Info
Financial
Info
Purchase History
Claim
History
Communication
History
Risk Appetite
New Insurance Needs
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ReservePrismCase Study: Cancer Patient Mortality Prediction
The Surveillance, Epidemiology, and End Results (SEER) research data (1972 – 2012)
Demographic(age, gender, race)
Diagnostic(time, tumor size,
type, location)
HistologicalMedical
TreatmentSurvivorship
Models: Linear, Logistic, KNN, CART, Random Forest, ANN
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ReservePrismCase Study: Cancer Patient Mortality Prediction
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ReservePrismCase Study: Cancer Patient Mortality Prediction
ROC Curve: Linear Regression
True Positive Rate
Tru
e N
egativ
e R
ate
0.0
0.4
0.8
1.0 0.6 0.2
ROC Curve: Logistic Regression
True Positive Rate
Tru
e N
egativ
e R
ate
0.0
0.4
0.8
1.0 0.6 0.2
ROC Curve: CART
True Positive Rate
Tru
e N
egativ
e R
ate
0.0
0.4
0.8
1.0 0.6 0.2
ROC Curve: Random Forest
True Positive Rate
Tru
e N
egativ
e R
ate
0.0
0.4
0.8
1.0 0.6 0.2
ROC Curve: KNN(5)
True Positive Rate
Tru
e N
egativ
e R
ate
0.0
0.4
0.8
1.0 0.6 0.2
ROC Curve: ANN(10,5)
True Positive Rate
Tru
e N
egativ
e R
ate
0.0
0.4
0.8
1.0 0.6 0.2
Receiver operating
characteristic curve:
0.5 is used as the threshold
for survival and death.
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ReservePrismCase Study: Cancer Patient Mortality Prediction
Breast Cancer
Linear CART
Variable Weight Variable Weight
Number of regional lymph nodes 32 Age at 2012 42
Age at Diagnosis 8 Age at Diagnosis 16
Number of regional lymph nodes removed or examined
7 Stage information 16
Surgery procedure of primary site 7 Tumor type (positive/negative) 9
Surgery type (site) 6 Insurance Status 4
Race 5 Primary site 2
Age at 2012 4 Reason for no surgery 2
Number of regional lymph nodes that were found to contain metastases
4 Tumor extension 1
Primary site and histology for children
4 Involvement of lymph nodes 1
Stage information 3 Number of regional lymph nodes that were found to contain metastases
1
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ReservePrismCase Study: Cancer Patient Mortality Prediction
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ReservePrismCase Study: Crime Classification
DataSan Francisco Police Department crime incident data
Goal: Given the time, address and geolocation of the
reported crime incidence, predict the crime type to allocate
appropriate resources.
Dates Category DayOfWeek PdDistrict Address X Y
2015-05-13 23:53 WARRANTS Wednesday NORTHERN OAK ST / LAGUNA ST -122.426 37.7746
2015-05-13 23:53 OTHER OFFENSES Wednesday NORTHERN OAK ST / LAGUNA ST -122.426 37.7746
2015-05-13 23:33 OTHER OFFENSES Wednesday NORTHERN VANNESS AV / GREENWICH ST -122.424 37.80041
2015-05-13 23:30 LARCENY/THEFT Wednesday NORTHERN 1500 Block of LOMBARD ST -122.427 37.80087
2015-05-13 23:30 LARCENY/THEFT Wednesday PARK 100 Block of BRODERICK ST -122.439 37.77154
2015-05-13 23:30 LARCENY/THEFT Wednesday INGLESIDE 0 Block of TEDDY AV -122.403 37.71343
2015-05-13 23:30 VEHICLE THEFT Wednesday INGLESIDE AVALON AV / PERU AV -122.423 37.72514
2015-05-13 23:30 VEHICLE THEFT Wednesday BAYVIEW KIRKWOOD AV / DONAHUE ST -122.371 37.72756
2015-05-13 23:00 LARCENY/THEFT Wednesday RICHMOND 600 Block of 47TH AV -122.508 37.7766
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ReservePrismCase Study: Crime Classification
Crime on the Map
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ReservePrismCase Study: Crime Classification
Feature Extraction
To use address in the prediction, words were counted and the frequent
ones were used in the classification.
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ReservePrismCase Study: Crime Classification
Prediction
Models used: Linear Discriminant Analysis, Logistic Model, K-nearest
neighbor, artificial neural network
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Q&A
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ReservePrismAbout Reserve Prism
ReservePrism is an advanced enterprise actuarial loss reserving, pricing and
predictive modeling platform.
The opinions expressed and conclusions reached by the presenter are his own
and do not represent any official position or opinion of ReservePrism.
ReservePrism disclaims responsibility for any private publication or statement by
any of its employees.
Visit us @ http://www.reserveprism.com.