1 estimating losses with predictive modeling: analytics careers at travelers institute for...

1

Estimating Losses with Predictive Modeling:Analytics Careers at TravelersInstitute for Mathematics and Its Applications

Catherine (Katy) A. Micek, Ph.D.March 3rd, 2013

Copyright © 2013 The Travelers Indemnity Company, Unpublished Work. All rights reserved.

22

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


3

My Career Path

• University of St. Thomas, 2000-2004

• University of Minnesota, 2004-2010

• Augsburg College, 2010-2012

• Adventium Labs, May – August 2011

• Travelers , June 2012 - present

• 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


44

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


55

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.

1. 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

2. 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.


66

Insurance 101: Data at Travelers

• Loss, Premium, and Financial Data

• Research & Development

• Unstructured

• Traditional Actuarial Usage

– Univariate analysis

• Includes external data

– Multivariate analysis

• Future development

– Continued use of sophisticated statistical methods

Example: Estimating Losses With Predictive Modeling


77

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.

X, the predictor

Y, th

e re

spon

se


88

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.

1. Frequency: what is the rate that claims are being made?

2. 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.

Oops! Why This Approach Doesn’t Work …


99

DO assume an exponential family distribution for Y

• 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)

Note: Non-normal distributions are more suited to highly skewed claim data

Gamma DistributionSource: “Gamma Distribution,” Wikipedia

Generalized linear models are one example of a suitable framework for our modeling goals.


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:1. Y can be from any exponential family of

distributions.2. Variance depends on expected mean.

• Approach: The parameters (a0, a1, …, an) can be estimated using maximum likelihood when underlying distribution is fixed.

Maximum LikelihoodSource: “A Practitioner's Guide to Generalized Linear Models”

10Copyright © 2013 The Travelers Indemnity Company, Unpublished Work. All rights reserved.

1111

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


1212

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


1313

References and Resources

• Travelers Careers– http://www.travelers.com/careers– Analytics Research Full Time Opportunities

• A Practitioner's Guide to Generalized Linear Models– http://www.towerswatson.com/assets/pdf/2380/Anderson_et_al_E

dition_3.pdf


http://www.travelers.com/careers



http://www.towerswatson.com/assets/pdf/2380/Anderson_et_al_Edition_3.pdf

http://www.towerswatson.com/assets/pdf/2380/Anderson_et_al_Edition_3.pdf

1 estimating losses with predictive modeling: analytics careers at travelers institute for...

Documents