1. Institute for Mathematics and Its Applications
Estimating Losses with Predictive Modeling: Analytics Careers at Travelers
Institute for Mathematics and Its Applications
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March 3rd, 2013
Catherine (Katy) A. Micek, Ph.D.

2. Agenda My Career Path Insurance 101 About Travelers
Business Impact of Loss Experience
Use of Data
GLMs: an Example of Estimating Losses with Predictive Modeling
Analytics at Travelers
AALDP
Questions
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3. My Career Path B.A. in Mathematics (2004)
Minors in Physics & QMCS
M.S. in Mathematics (2008)
Ph.D. in Applied Mathematics (2010)
Visiting Assistant Professor
Taught undergraduate math courses
Visiting Professor
Error analysis in FEM method
Sr Consultant, Research & Analytics
Predictive Modeling for Business Insurance
University of St. Thomas,
University of Minnesota,
Augsburg College,
Adventium Labs, May – August 2011
Travelers , June present
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4. Insurance 101: Travelers Who are we?
Travelers is a property and casualty insurance company that sells a wide variety of insurance and surety products and risk management services to businesses, organizations, and individuals.
What do we sell?
Our principal products are insurance policies and surety bonds, which are, in essence, promises to pay in the event that customers experience certain types of losses.
How do we use mathematics?
The unique challenge in insurance is that we don’t know what the cost of insuring a customer is when we sell the policy, so we use mathematics to predict the expected losses for groups of customers.
Example: The cost to insure an auto customer
It’s impossible to predict if someone is going to …
Get into an accident
The type of accident (hit a telephone pole, hit another vehicle, bodily injury)
How bad (cost) the accident will be
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5. Insurance 101: Business Impact of Loss Experience
When looking at the business impact of loss experience, there are two fundamental questions that need to be answered.
Ratemaking: looking to the future
Setting rates for policies
How much do we need to charge customers for a policy in order to reach our target profit? Basic idea: price = cost + profit
Reserving: looking at the impact of past experience
Setting aside reserve money
How much money do we need to set aside to pay for claims?
To answer these questions, we must do data analysis.
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6. Insurance 101: Data at Travelers
Traditional Actuarial Usage
Univariate analysis
Includes external data
Multivariate analysis
Future development
Continued use of sophisticated statistical methods
Loss, Premium, and Financial Data
Research & Development
Unstructured
Example: Estimating Losses With Predictive Modeling
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7. First Model Attempt: Multiple Linear Regression / Ordinary Least Squares
E[Y] = a0 + a1X1 + …+ anXn
Goal: Fit a linear relationship between the predictors (X1, …, Xn) and the response variable Y.
Assumptions:
1. Y is normally distributed.
2. The variance of Y is constant.
Approach: The parameters (a0, a1, …, an) can be estimated by minimizing the sum of squared errors.
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8. Oops - DON’T assume Y is normally distributed
Oops! Why This Approach Doesn’t Work …
Oops - DON’T assume Y is normally distributed
In insurance, we study loss experience in terms of claims.
Two aspects of claims must be considered.
Frequency: what is the rate that claims are being made?
Severity: what is the average size of claim?
The underlying distribution in the model depends on what aspect of the loss experience we’re investigating.
Double Oops - DON’T assume the Variance of Y is constant
High frequency losses have less variance.
High severity losses have more variance.
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9. DO assume an exponential family distribution for Y
Note: Non-normal distributions are more suited to highly skewed claim data
Poisson - claim frequency
Discrete distribution
Time-invariant
Variance equals mean (m = E[Y])
Gamma - severity
Continuous distribution
Variance equals mean squared (m2 = E[Y]2)
Generalized linear models are one example of a suitable framework for our modeling goals.
Gamma Distribution
Source: “Gamma Distribution,” Wikipedia
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10. Generalized Linear Models
For generalized linear models, we have that
E[Y] = g-1(a0 + a1X1 + …+ anXn)
where g(x) is the link function.
Goal: fit a non-linear relationship between the predictors (X1, … , Xn) and the response variable Y.
Assumptions:
Y can be from any exponential family of distributions.
Variance depends on expected mean.
Approach: The parameters (a0, a1, …, an) can be estimated using maximum likelihood when underlying distribution is fixed.
Maximum Likelihood
Source: “A Practitioner's Guide to Generalized Linear Models”
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11. Analytics at Travelers
Our problems are challenging in their scope and interdisciplinary nature.
Written and verbal communication skills are important
Lifelong learners
The analytics group at Travelers is a large (300+) and diverse community.
Bachelors, Masters, Ph.D.s
Mathematics, statistics, physics, actuarial science, computer science, business
Ph.D.s are a valuable asset within the Travelers analytic community!
Creative and experienced problem-solvers
Ability to see the “big picture” and stream-line processes
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12. Actuarial & Analytics Leadership Development Program (AALDP)
5-yr program for actuarial students and analytics participants
Actuarial students offered exam support
Analytics participants learn insurance on the job through work projects and seminars (exams are optional)
Leadership development opportunities
Career exploration opportunities through rotations
Networking opportunities (mentor program, committees)
2012 – Pilot Class for Analytics Participants
Offers a flexible career path
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13. References and Resources
Travelers Careers
Analytics Research Full Time Opportunities
A Practitioner's Guide to Generalized Linear Models
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