Once Upon a Time

By Rebecca L. Adcock

Introduction

I have a lot of “once upon a time” stories I could tell (just ask my sons) but the one I want to tell here is all about mathematics. Of course, it starts out…

Once upon a time I graduated from the University of Georgia with a Bachelor of Arts degree in mathematics and computer science. I figured with that kind of degree I would work at some kind of research facility that needed a person with math knowledge to code programs analyzing data gathered from experiments, et cetera. Guess what? Those jobs were scarce but there were numerous jobs in businesses for people with those same skills. I was hired fresh out of college by an upstart automobile insurance company. When I was hired, Atlanta Casualty Company had approximately 65 employees and wrote insurance in one state (Georgia) and when I left the company had grown to over a thousand employees and was licensed in over twenty states. I started as the company’s first full-time programmer and when I left I was a manager in the M.I.S. department.

In the mid 1990’s, Atlanta Casualty was one of Gwinnett county’s top employers. For most of my tenure with the company, we were located in the Myrick Building, later called the DAV Building, and now called Jefferson Plaza, at the intersection of Peachtree Industrial Boulevard and Holcomb Bridge Road in Norcross. How ironic that the intersection was named one of the worst intersections in Gwinnett County because of the number and severity of automobile accidents occurring there. I remember standing in the Accounting Department on the fourth floor and watching emergency personnel work a fatal crash. It was a real-life lesson of why we did what we did. Anyway, Atlanta Casualty is now part of Infinity Insurance and the offices have moved to the Alpharetta area.

What Is Insurance?

When I first started working at Atlanta Casualty, I knew as little about automobile insurance as most twenty-somethings. I knew I paid premiums twice a year and it seemed like I got nothing in return. Between my new employment and a wreck I had shortly after I started working, I learned real fast what insurance was all about.

An insurance policy is a legal binding contract between an individual and an insurance company. In some cases an agent acts as an intermediary between the individual and the company. An independent agent can sell insurance policies from any number of companies and a reputable agent will use his expertise to match his customer to the company that best suits him, based on a number of factors, including driving record, driver’s age, vehicle horsepower, and cost of the car when new. Younger drivers cost more to insure than experienced drivers, and sports cars more than station wagons. Previous traffic violations tack points onto the driver’s statistics and each point costs more in premium. A minor infraction would add one point and a moving violation like speeding could add 3 points.

The money the customer pays for the insurance, the premiums, goes into an account controlled and administered by the insurance company. When a customer (the ‘insured’) suffers a loss, the company (the ‘insurer’) compensates the insured based on the coverage described in the policy. In the state of Georgia, liability insurance is required by law. Liability coverage protects the victim in an automobile accident, the party who was not ‘at fault’. An insured may also buy physical damage coverage, which would cover his own vehicle even if he is at fault.

What most people don’t know about automobile insurance companies is that most of the money collected as premiums is paid back to cover losses. A typical loss ratio could run more than 94 cents on the dollar. To create a profit, an insurance company has to put together a team of savvy employees, ranging from investment brokers to experienced actuaries. An actuary analyzes the company’s history of losses and decides who costs the most to insure. Typically younger drivers suffer from the most accidents and therefore cause the company to pay out more money. Consequently, the younger drivers would pay higher premiums for coverage.

Mathematics in an Insurance Company?

Maintenance-Free and Accurate Code

I was hired as a programmer at a time when Atlanta Casualty was creating all their own software applications in-house. I learned pretty fast that knowing some math really paid off when I was writing code. In the world of programmers, there are two kinds of tasks. The fun stuff is creating new programs and systems. The crummy job is maintaining code, yours and others’. The best way to keep maintenance to a minimum, so you don’t get stuck maintaining it, is to write efficient code. Given a choice between storing data that has to be updated infrequently in a table or creating an algorithm to produce the data, you are better off to create an algorithm that doesn’t need updating. That way you don’t risk forgetting to maintain the table and end up sending out checks to customers who didn’t warrant a return premium. Two problems with that scenario… the bosses aren’t happy…and … try getting that money back from the customer! If the data is volatile, like insurance premiums which can be altered twice a year, the programmer can choose to use tables so code doesn’t have to be changed and retested frequently.

y=cos x

y=2cos 2x

Let me digress for a moment and mention the similarity between testing a code change and changing a mathematical equation. If you are teaching the function y=cos x to a class and you change the function to y=2cos 2x, the students can’t tell which ‘2’ caused which change in the graph. Did the ‘2’ in front of ‘cos’ cause the height of the curve to change or did it cause the curve to repeat more frequently over the same interval? Programming and testing code is similar. I learned to change one parameter at a time and test it before making another change. It may take a little longer but the result is consistent, accurate code.

Designing a Database

Besides creating custom code, programmers at Atlanta Casualty also designed and built their own database, including the data retrieval system. Prior to creating the database, we researched what data needed to be captured, the size of each field, whether the field was alpha or numeric. For instance, we reserved 15 characters to store the driver license number. At the time, most states had a driver license number based on the 9-digit social security number. The most glaring exception was New York, which had a license number of approximately 20 characters. We were assured by the Vice-President of Product Development that we would write insurance in New York over his dead body so we set the field at 15 characters. Numeric fields could be stored as ‘packed’, or ‘double-density’, to save space. We were working on a mainframe and data storage was more expensive and fields were fixed, not delimited by special characters, so field sizes and storage techniques were important to the overall cost of the project and to the budget of a small and growing company. We only stored what could not be recreated from other data. It was considered a waste of space to store anything that could be derived from other fields.

Another consideration was the size of each record. Just as data fields were fixed in size, so were data records fixed in size. For disk storage efficiency, a collection of records needed to end at the end of a word boundary. The Burroughs (and later Unisys) systems we worked on were based on an 8-byte word and the disk was allocated on a multiple of 8 and 180. If the records were not evenly divisible then segments of the disk would be wasted.

For a brief tour of disk storage, follow this link. To get back to this page, use the browser’s back arrow. http://www.computermuseum.li/Testpage/Disks-Compared.htm

The picture above (on right) predates my M.I.S. experience (not by much, though).

Probability vs. Evidential Data

When we think of auto insurance, we may wonder about our probability of being in a crash. Auto insurance companies don’t deal with the mathematical intricacies of the probability of an accident occurring to a particular person in a certain car at a specific location or date. The actuaries scrutinize the data the company has collected over a period of time to determine how much money has been paid out for each premium dollar collected for a particular driver or vehicle. They will look at the following:

· the driver’s age.

· the territory. This is where the insured lives or garages the car. Metropolitan areas have higher premiums than rural areas.

· the points on the drivers’ record.

· the symbol and age of vehicle. Symbol is based on classification of the car as luxury, sports car, etc. Industry data on the cost to repair the vehicle is also considered in determining the symbol assigned to a model.

If the company has paid out $1.07 in losses for each $1.00 collected in premiums for a particular class of drivers, the actuary may increase the premiums for the class. This can do two things – the increased premiums will cover the losses or that class of insured may place their business elsewhere. The actuary walks a tightrope between keeping the company in the black by collecting enough premiums to cover losses and trying to keep the premiums competitive with other companies.

Flowchart of part of the actuarial system.

Data Integrity

Based on what you just read in the previous section, you can see that the integrity of data is very important to an insurance company. What we found out as we collected this data was that the accuracy of our data seemed to deteriorate as our data bank grew. We had more programmers on staff so there were more ‘cooks in the kitchen’. We were collecting more data than we ever had before. We needed to establish better controls on all of our data. We had always had balancing procedures and standards for the billing and accounting systems so now we established balancing standards on all systems that fed data into the actuarial database. We knew from experience that we would never be able to balance the premiums to the penny. We had data coming from multiple systems and rounding discrepancies and minor errors were a fact of life. We needed to know that we had not committed operational errors while collecting the data or programming errors while maintaining code and senior management needed reassurance that we knew what we were doing. We established a margin of error that was acceptable to us and to senior management. Now we could balance the system to our controls; if our results were within our accepted margin, we released the results to the actuarial department. If we exceeded the acceptable margin, we returned the system to the programmers and operators.

The End of the Story

I eventually left Atlanta Casualty company and went to work for a company called EMS Technologies, also in the Norcross area. I left there to open a retail franchise with my husband and when he passed away, I returned to my first love – the desire to teach math. I enrolled in the Master’s degree math education program at the University of Georgia in August, 2004. In April, 2006, I accepted a teaching position in a Gwinnett County high school and I look forward to starting my new career in August.

As I look back over my previous professional lives, I see that mathematics always played a significant role. When Bill and I were running our little business, we used math everyday, calculating customer discounts, balancing the store’s accounts, ordering product… But wait… that’s a whole other ‘once upon a time…’.

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