**Session 35 PD, Predictive Modeling for Actuaries: Integrating Predictive **
**Analytics in Assumption Setting **

**Moderator: **

**David Wang, FSA, FIA, MAAA **

**Presenters: **

**Guillaume Briere-Giroux, FSA, MAAA **
**Eileen Sheila Burns, FSA, MAAA **

### Presented by

### Eileen S. Burns, FSA, MAAA

### Milliman

October 27, 2014

**Integrating Predictive Modeling in **

**Assumption Setting**

**What makes predictive modeling different?**

### Results

– More granularity – Quantifiable goodness-of-fit### Foundations

– Different tools – More data prep**BUILDING A SOLID **

**FOUNDATION**

**Human and physical capital**

### Decision #1: Project staff

– Actuary – Statistician

### Supporting staff

### Decision #2: Program

– Comfort – Flexibility – Processing efficiency – Cost### Computing resources

**OR**

**?**

**q**

_{x}

_{x}

### ∑x

### 2

**OR**

**?**http://commons.wikimedia.org/wiki/File:SAS_logo_horiz.svg http://commons.wikimedia.org/wiki/File:R_logo.svg

**Exploratory data analysis**

### Programmer, statistician, and actuary

### Data visualization tools

http://commons.wikimedia.org/wiki/File:SAS_logo_horiz.svg http://commons.wikimedia.org/wiki/File:R_logo.svg http://commons.wikimedia.org/wiki/File:Tableau_Software_Logo_Small.png

How is each field distributed? Is it consistent over time?

Which variables are related to the target variable, and how?

**Data visualization – on raw and prepped data**

**Policy value**
**Policy value**
**Category**
**Category**
**Time**
**Time**

**Example 1: Gender**

**Problem: Missing **

### extreme number of

### genders, male and

### female counts

### unexpected

**Solution: Code **

### problem referencing

### secondary insured

### by mistake (gender2

### vs. gender field)

**MALE**

**FEMALE**

**NA**

**Example 2: Distribution channel**

**Problem: Large **

### number of distribution

### channels missing

**Solution: No **

### change. Discovered

### issue by looking

### across time. Fix is

### only available for

### policies that don’t

### lapse, and would

### distort experience.

**Example 2: Distribution channel**

**Problem: Large **

### number of distribution

### channels missing

**Solution: No **

### change. Discovered

### issue by looking

### across time. Fix is

### only available for

### policies that don’t

### lapse, and would

### distort experience.

**08**

**Q2**

**08**

**Q3**

**09**

**Q1**

**08**

**Q4**

**09**

**Q2**

**09**

**Q3**

**09**

**Q4**

**10**

**Q1**

**10**

**Q2**

**A**

**B**

**C**

**NA**

**Example 3: Policy status records**

**08**

**Q2**

**08**

**Q3**

**09**

**Q1**

**08**

**Q4**

**09**

**Q2**

**09**

**Q3**

**09**

**Q4**

**10**

**Q1**

**10**

**Q2**

**Problem: No deaths **

### in any Q4

**Solution: No **

### change. A data issue

### with no feasible

### solution. Only affects

### scaling and only for a

### small percentage of

### policies.

**Example 4: Rider prevalence**

**08**

**Q2**

**08**

**Q3**

**09**

**Q1**

**08**

**Q4**

**09**

**Q2**

**09**

**Q3**

**09**

**Q4**

**10**

**Q1**

**10**

**Q2**

**Problem: no other **

### rider features seen in

### one quarter.

**Solution: Analyzed **

### prior and subsequent

### quarters to identify

### policies with riders.

### Necessary to avoid

### modeling policies

### with riders as no-rider

### policies.

**Example 5: Assessing policy values**

**Death benefit**

Log distribution

**Log death benefit**

Relative distribution
**DB/AV** **% of dist**
<= 1.00 25%
1.01 - 1.25 50%
1.26 - 2.00 10%
2.01 – 5.00 5%
5.01 – 9.00 5%
9.01+ 5%

**Problem: What is a **

### reasonable

### distribution?

**Solution: Check log **

### distribution, and

### check relative to

### similarly-scaled field.

### Led to recognizing

### some $4$ benefits,

### and some DB coded

### as increase over AV.

**Example Recap**

### Response variable

– Policy status### Factor variables

– Rider prevalence – Gender – Distribution channel### Numeric variables

– Policy value distributions

### Correlations

### Other issues

– Missing entire files

– Files with misleading names (e.g. wrong valuation date) – Inconsistent feature

descriptions (e.g. reset/ratchet) – “unreliable” fields

**Takeaway: every variable that is part of a typical **

experience analysis has required specific attention to ensure consistency and model validity, as have each of the additional 50+ fields.

**Thank you!**

Eileen S. Burns, FSA, MAAA Milliman

eileen.burns at milliman.com 206-504-5955

### Predictive Modeling Case Studies

**Liz Olson, FSA, MAAA**

### Background

• I am not:

– A statistician

– A model builder

– Responsible for experience studies

• I am:

– An actuary

– Responsible for assumption governance

– Someone who knew there was power in statistics, but spent years

before finding the right statistician to pull it off

### Experience Studies Where We’ve Used Predictive Modeling

• Variable Deferred Annuity Lapses

• Deferred Annuity Mortality

Fixed Deferred Annuity Lapses

VUL Life Insurance Mortality

Life Insurance Renewal Premiums

### Fixed Deferred Annuity Lapses

• Examined Fixed Deferred Annuity lapses using predictive modeling for

the first time in 2013

• Some factors that lapse behavior varied by were:

– Attained Age

– Policy Size

– Effective Surrender Charge

– Difference between credited rate and market rate

– Qual vs. Non-Qual

– Guarantee Minimum Floor Rate

• These drivers also had different sensitivities depending on whether the

policy was in the surrender charge period, in the shock year, or in the post-shock years

### Fixed Deferred Annuity Lapses

• Typical graphs of dynamic parameters

• Predictive modeling allows for better delineation between base and dynamic lapses

**Dyn**
**am**
**ic**
** Fa**
**ct**
**o**
**r**
**Policy Size**

In CDSC Shock Post Shock

Smaller Larger **Dyn**

**am**
**ic**
** Fa**
**ct**
**o**
**r**
**Attained Age**

In CDSC Shock Post Shock
Younger _{Older}

### Fixed Deferred Annuity Lapses

• Progression of Models – Base Lapses Only

5
**La**
**p**
**se**
** Ra**
**te**

**Actual Lapse Rates vs. Model Over Time**

Actual
Model: Base Lapses Only
### Fixed Deferred Annuity Lapses

• Progression of Models – Base and Some Dynamic Parameters

6
**La**
**p**
**se**
** Ra**
**te**

**Actual Lapse Rates vs. Model Over Time**

Actual
Model: Base + Some Parameters
### Fixed Deferred Annuity Lapses

• Progression of Models – Final Model

7
**La**
**p**
**se**
** Ra**
**te**

**Actual Lapse Rates vs. Model Over Time**

Actual
Model: Final
### Fixed Deferred Annuity Lapses

Lessons Learned

– Just because the model fits the past doesn’t mean it’s good for predicting

the future

– The model told us that for one product the difference between our credited

rate and the market rate didn’t matter for policy durations post shock

• The study had a few years of experience, but all in low rate environment

– Don’t rely on the model but rather use it to inform decision making

– Involve actuarial modelers early on to ensure the dynamic parameters are

implementable

– “Language barrier” between statisticians and actuaries

### VUL Life Insurance Mortality

• We worked with a consulting firm to analyze our VUL mortality

experience using predictive modeling

• In addition to analyzing mortality across the obvious dimensions (age,

gender, underwriting category, etc.) we were also able to gather data from our P&C business or from other sources

– Home size, number of people in household, automobiles

– Interests of individuals in the household (i.e. boating, skiing, scuba, golf, organic foods, interior design, video games…)

• Consultant was able to tease out two profiles with very different

mortality experience

– Profile A: More attributes lead to lower mortality

– Profile B: More attributes lead to higher mortality

### VUL Life Insurance Mortality

Customer Profile A Customer Profile B

0
0.5
1
1.5
0 1 2 3 4+
**M**
**o**
**rt**
**alit**
**y **
**R**
**e**
**la**
**ti**
**vi**
**ty**
**Number of Attributes of Profile A**
**Relative Mortality by Number of **
**Profile A Attributes**
0
0.5
1
1.5
2
2.5
0 1 2 3 4+
**Mo**
**rt**
**al**
**it**
**y **
**Re**
**la**
**ti**
**vi**
**ty**
**Number of Attributes of Profile B**
**Relative Mortality by Number of **
**Profile B Attributes**
10

### Life Insurance Renewal Premiums

• New project to use predictive modeling to establish renewal premium

assumptions for ULSG and VUL products

• Could ultimately be used as a retention strategy to proactively notify

customers who the model suggests may have a higher likelihood of stopping or reducing their premiums

### Life Insurance Renewal Premiums

• Some companies may be setting this assumption in a very simplistic

manner (i.e. all policies make renewal premiums such that the aggregate matches expectations)

• This can lead to a sizeable error on many policies

12
**Histogram of Actual vs. Predicted **
**Renewal Premium Error**
All PHs Pay Average
No Error Large Error
Large Error
Po
lic
y
C
o
unt

### Life Insurance Renewal Premiums

• Our new approach using predictive modeling has further improved our

renewal premium assumption

13
**Histogram of Actual vs. Predicted **
**Renewal Premium Error**
Predictive Modeling
Bucketing Algorithm
All PHs Pay Average
No Error Large Error
Large Error
Po
lic
y
C
o
unt

### Other Possible Areas for Predictive Model Use

• Living Benefit Utilization

• Transfers between Fixed and Variable investments

• Life Insurance Surrenders

• Life Underwriting Decisions

• 401k, 457, 403b Case Lapses and Participant Deferrals

• Sales Distribution Tendencies

– Could possibly identify producer abuse such as STOLI or STOVA

### Data Quality

• ASOP 23 provides insights into what an actuary should do when using

data

– Review data for reasonableness and consistency

– Not required to audit the data

• Some steps that we’ve taken

– Compare to ledger sources (policy count, deaths, lapses, FY

premium, renewal premium, claims)

– Cursory review of distributions (issue age, account value, face

amount, gender, underwriting category)

### Staffing Model

• Pure statisticians often don’t have the product background or

business intuition needed

• Actuaries often don’t have the statistical horsepower needed

• Finding someone with both of these is rare

• Leaders could staff by:

– Using pure statisticians to build the predictive models and

using actuaries to manage the projects and add insights based on their intuition and experiences, or

– Grow the statistical talent by sending actuaries through

extensive statistical training so they can run the predictive modeling project from start to finish

### Summary

• Seemingly endless possible uses of predictive modeling in

experience studies

• Think beyond just using traditional internal data

• Garbage In = Garbage Out

• Build the right team

**Guillaume Briere-Giroux, FSA, MAAA, CFA **

### Integrating Predictive Analytics in Assumption Setting

Implementation and Integration in Financial Models 2014 SOA Annual Meeting & Exhibit

### Agenda

I. How and where predictive analytics impact assumption setting?

II. Implications for assumption setting process

III. Challenges and solutions for financial modeling integration IV. Key takeaways

### How predictive analytics impact assumption setting?

**B**

**u**

**si**

**n**

**ess**

**v**

**a**

**lue**

**Data analytics literacy**

**Describe / monitor**
**Analyze / understand**
**Score / predict**
**Decide / optimize / **
**manage**
Descriptive analytics

*(what happened and why?)*

Predictive analytics

*(what will happen?)*

Prescriptive analytics

*(what should we do?)*

**Scope of predictive modeling techniques**
**Enhanced **
**experience studies**
**Enhanced **
**assumption setting**
**Enhanced **
**model-based**
**decisions**

### Where predictive analytics impact assumption setting?

Use of predictive modeling is increasingly widespread for experience studies

**Product** **Surrenders / **
**Lapses**

**Utilization / funding **

**pattern** **Mortality** **Morbidity**

VA Living Benefits

###

###

###

FIA Living Benefits

###

###

Fixed Annuities

###

###

Universal Life

###

###

###

Term

###

###

Long Term Care

###

###

###

We are also seeing greater use of predictive analytics in M&A

### Implications for assumption setting process

**1**

**More attention is paid to more secondary internal variables**

**2**

**Increased opportunities to test external variables**

**3**

**Additional relationships to study and understand**

**4**

**More comprehensive ”data-driven” discussions**

**5**

**Better ability to put experience in context**

In summary, using predictive analytics requires more resources dedicated to assumption setting but enables richer thinking around key assumptions

### Example: Integrated GLWB policyholder behavior cohorts

**Cohort of GLWB** **Observed behavior**

**“Efficient” users** • Utilize 100% of GLWB maximum income
• Strong utilization “feature skew”

• Low lapse rate

• More efficient dynamic lapses

**“Partial” users** • Utilize less than 100% of GLWB maximum income
• Weaker utilization skew

• Higher lapse rate than efficient users • Less efficient dynamic lapses

**“Excess” users** • Utilize more than 100% of GLWB maximum income
• Very high lapse rates

• Least efficient dynamic lapses

**“Waiting” users** • Have not yet utilized
• Low lapse rates

• Efficient dynamic lapses • Waiting for rollup?

### Computational implications for modeling

Run time optimization becomes a three dimensional problem

Can specify accuracy functions to determine optimal accuracy for a given run time and generate an efficient frontier

### Other considerations for modeling

How granular should the model become?

**1**

**Materiality and certainty of dynamic**

**2**

**Materiality of business**

**3**

**Model purpose**

**4**

**Degree of buy in**

### Model implementation approach

There is a compromise between transparency, flexibility, controls and system performance

**Desirable property** **Parameterized formula** **Factor tables**

**Transparency**

**Flexibility (model form)**

**Flexibility (adjustments)**
**Ease of control**
**Auditability**
**Computational performance**
High
Low

### Best practices for model implementation

**Area of focus** **Considerations**

**Parallel testing** • New assumptions are more complex to code
• Do single cell-testing with replicator (e.g., Excel)

• Excel replicator can also be used for extreme value testing / sensitivity testing

**Internal data** • Data definition between experience study and financial models must be
consistent

**External variables** • Modeler must understand the sensitivity of projected behavior to external
variables (how reliable are my scenarios?)

**Sensitivity testing** • Understand the potential impact from stress testing the assumption
parameters

**Documentation** • Documentation of rationale for key modeling decisions and any
limitations or simplifications

### Key takeaways

**1**

**Think about the business and the environments**

**2**

**Think about the models and their end goal**