Evolving Techniques and Capabilities: Part 2

Looking ahead, what kinds of models might become commonplace in the next 25 years? One area to explore is interactive computer technology, i.e., what we know today as computer games on CD-ROM. I haven't played interactive computer games myself, being somewhat of an iconoclast. My son, on the other hand, loves his Gameboy and his Gamecube, and it's only a matter of time until he discovers the treasure trove of interactive games on the Internet. One game he likes now is a simulation game in which he tries to build a marine-based theme park. (To my eye, the game is an incredibly complex advertisement for a particular sea-based theme park!) The player's overall goals are to maximize net income and customer satisfaction. The computer screen shows the current layout of the park-attractions, attendees, park staff, walkways, and parking areas. Attractions can be moved around and walkways can be installed or removed to adjust traffic flow. The game keeps track of revenues and expenses.

Customers come to the park and pay admission (and other) fees. Ongoing expenses include staff salaries and the cost of maintenance and repairs. As (and if) capital increases, funds become available to construct new facilities and attractions. These can bring in more attendees, which generates more revenues.

Now substitute "insurance company" for "theme park." Substitute "policyholders" for "attendees." Add various department modules (underwriting, claims marketing, and so on) and whatever bells and whistles would make the game more realistic. Players would include a CEO, the department heads, and an Appointed Actuary (choose in-house or outside consultant). The software would keep track of premiums and losses, as well as revenues and expenses. In order to write more business, underwriters would have to be hired and "trained." As the number of claims increased, additional claims adjusters would need to be hired and "trained." (Training takes time and is not always 100% successful. While new staff are trained, current staff must strain to meet production schedules. So the game would incorporate time lags with probability distributions.) The game would generate data for the different players to analyze and allow them to make decisions about strategy and tactics. It could even prepare statutory and GAAP financial statements!

This sort of "model" casts a whole new light on the notion of management training. Actuaries would learn to be CEOs in their spare time!

A related modeling area to explore might be called time-dependent models or rule-based models. Stephen Wolfram, who designed the Mathematica software, discusses his research along these lines in his book A New Kind of Science, published by Wolfram Media Inc. in 2002. This book summarizes Wolfram's findings after 20 years' work studying the behavior of relatively simple cellular automata models (and other models that he shows are closely related to cellular automata models.) I don't mean to write a book review, but I will point out that this book, while quite readable, is not summer reading at the beach. In addition to almost 850 pages of text, Wolfram includes almost 250 pages of chapter notes and comments that are printed in the smallest font I've ever seen in a published text. The author displays an overwhelming knowledge about virtually all areas of science and mathematics.

Financial models today are notoriously poor at predicting turning points... what should we do instead?

Wolfram's basic model consists of an infinite grid of squares that are colored black or white. Each row can be thought of as representing a discrete moment of time, and all squares below the first row are white. Each row represents a discrete point in time. The first row, t=0, has squares that are arbitrarily colored white or black. The color of each square in the second row depends on the colors of the squares in the first row that are near it, according to a predetermined rule. For example, one simple rule is "a square at time = t +1 is colored black if at least two of the three squares touching it are black, otherwise the square is white." Now apply the same rule to color the squares in the third row based on the colors of the squares in the second row, and repeat ad infinitum. Finally, step back, look at the overall patterns that have emerged on the grid, and try to characterize the patterns you see.

The author created grids for a huge collection of rules, and the book includes pictures of them. Some grids are not especially interesting-the grid turns all black or all white after a few iterations, for example. Other grids show interesting structures of triangle (and other) shapes that never exactly repeat themselves. You can't predict exactly what will appear on the grid in subsequent iterations, but you can make probabilistic statements about how often certain shapes will pop up. Still other grids appear to be completely unpredictable, even chaotic-the only valid prediction you can make about the patterns yet to emerge is that you probably haven't seen them in previous iterations.

If cellular automata models seem too simple to be useful, consider that the author manages to explain relativity theory with a cellular automata model. He also extends his basic model by using a higher-dimensional grid, permitting more colors, and setting rules that have random elements in them. What fascinates me in his work is that, probabilistic elements aside, so many of the rules generate patterns that are almost completely unpredictable, yet every model is completely deterministic. Wolfram shows that equations and curves-even axiomatic underpinnings-do not apply to these models. The only way to analyze one is to actually run it on a computer and see what happens.

Now consider modeling the behavior of a collection of individual financial decision-makers who act based on information they gather about the past and the present. Even though they may act in a manner that is completely deterministic-behaving as cellular automatons, if you will-strange and completely unpredictable things manage to happen in the economy.

This sounds to me like a promising line of inquiry. Financial models today are notoriously poor at predicting turning points. By going outside the "theorem-proof style" of mathematics we learned in school, Wolfram may be pointing a way towards understanding whether we can answer these questions; and if so, how; and if not, what should we do instead?

I wish I could come back in a hundred years and find out. I'll bet the computer games will be really cool.