Ruark Consulting Tim Paris Presenter Zimin Zhuang A Business Problem I Introduction and Objective Objective Models Data Goldenson Innovation Introduction and Objective Objective Construct a ID: 651485
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Slide1
Predictive Modeling for
Variable Annuity Policyholder Behavior
Ruark Consulting: Tim Paris
Presenter: Zimin Zhuang Slide2
A Business Problem?Slide3
I. Introduction
and ObjectiveObjective
Models
Data
Goldenson InnovationSlide4
Introduction and
ObjectiveObjective
Construct a
series of company specific
variable
annuity
partial withdrawal predictive models.
Predictive
modeling uses historic data to identify patterns which can be used to predict future
behavior.
P
redictions
are then used to inform business decisions Slide5
Introduction and
ObjectiveFrequency-Severity
Model
Claim Frequency
–
a
probability
,
indicating the
probability
that
the
i
th
policyholder
partial withdraws.
Claim Severity
– a continuous variable indicating the amount of a
partial withdraw.
Predicted Withdrawal Rate
=
Claim Frequency
x
Claim Severity Slide6
Introduction and
ObjectiveData
Industry
partial withdrawal
data
over
a dozen
companies
.
R
epresentative seriatim monthly data
since 2009.
C
omprising
about
10 million
records
.Slide7
Introduction and
ObjectiveDataSlide8
Introduction and Objective
Goldenson InnovationSlide9
Introduction and Objective
Goldenson InnovationCapture historical
behavior into the modeling
Provide
company specific
adjusted model.Slide10
Introduction and Objective
Goldenson InnovationHistorical variables are used to capture individual behaviors from past
.
Frequency
-
Historical percentage
of partial withdrawals for frequency.
Severity
-
Historical Mean
.
Severity
-
Historical Slope
. Slide11
Introduction and Objective
Goldenson InnovationSlide12
II. Model Development
Framework & ProcessCutoff Point
Industry Model
Company Model
Company Adjusted Process
Company Adjusted ModelSlide13
Model
DevelopmentRobust
Statistical
FrameworkSlide14
Model
Development
Cutoff point
According to our modeling assumption
– Claim
Frequency
has
a
binomial
distribution
–
Logistic regression
is used to predict binomial data
Minimize random noise
in frequency model.
Convert
continuous
frequency predicted value
back to
binary
frequency value
.
Improving
aggregate result.Slide15
Model
DevelopmentCutoff Point Example
Actual Value
Predicted (Both Face Amount = 100)
A/E
Actual Frequency
Actual Severity
Actual PW
Predicted Frequency
Predicted
Severity
Predicted PW
112.78%
1
40%
40%
80%
42%
33.6%
1
50%
50%
90%
48%
43.2%
0
0%
0%
30%
10%
3%
Actual Value
Predicted (Both Face Amount = 100)
A/E
Actual Frequency
Actual Severity
Actual PW
Predicted Frequency
Predicted
Frequency
(After
0.5 Cutoff )
Predicted
Severity
Predicted PW
100%
1
40%
40%
80%
1
42%
42%
1
50%
50%
90%
1
48%
48%
0
0%
0%
30%
0
10%
0%Slide16
Model
DevelopmentIndustry Model Performance*
*Artificial
numerical example
for present purposes only.
Industry Model 5 fold Cross validation Results
Industry Model
A
/
E
A
/
E
A/E
A/E
A/E
Average A/E
Average Error
LT
100.00%
101.10%
102.30%
98.90%
99.00%
100.26%
0.011
GT
102.50%
101.13%
101.20%
100.90%
99.25%
100.30%
0.01296
Full
99.00%
98.25%
99.12%
99.13%
98.26%
100.30%
0.01248Slide17
Model
DevelopmentCompany
Model Performance*
*Artificial
numerical example
for present purposes only.
Company
Model 5 fold Cross validation Results
Industry Model
A
/
E
A
/
E
A/E
A/E
A/E
Average A/E
Average Error
LT
102.00%
99.10%
103.30%
97.90%
98.00%
99.58%
0.0206
GT
101.30%
102.13%
101.15%
100.00%
99.88%
100.89%
0.0094
Full
98.00%
99.75%
99.27%
99.38%
98.99%
99
.
08
%
0.00922Slide18
Model
Development
Company Adjusted
ProcessSlide19
Model
Development
Company Adjusted
Process
Industry coefficient is
within
the company’s confidence interval: the
industry’s coefficient
is
used.
Slide20
Model
Development
Company Adjusted
Process
Industry coefficient is
greater
than the company’s confidence interval upper bound: use the company’s
upper
bound
.
Slide21
Model
Development
Company Adjusted
Process
Industry coefficient is
smaller
than the company’s confidence interval lower bound: use the company’s
lower bound
.
Slide22
Model
DevelopmentCompany Adjusted
Model Performance*
*Artificial
numerical example
for present purposes only.
Company
Model 5 fold Cross validation Results
Industry Model
A
/
E
A
/
E
A/E
A/E
A/E
Average A/E
Average Error
LT
101.00%
100.00%
101.00%
99.00%
99.00%
100.00%
0.008
GT
101.31%
101.12%
98.15%
100.39%
99.24%
100.04%
0.01086
Full
99.00%
99.85%
99.26%
99.34%
100.00%
99.49%
0.0051Slide23
III
. Future ImplicationsA
pply
the method to different lines of
business.
Fixed index
variable
annuities.
Life insurance mortalities.
Healthcare products.
…Slide24
Presenter
Information
Zimin
Zhuang
M.S. in Biostatistics
M.S. in Applied Financial Mathematics (Candidate)
Janet & Mark L. Goldenson Center for Actuarial Research
University of Connecticut
zimin.zhuang@uconn.eduSlide25
Questions？
Thank You!