Modeling Ponzi Schemes

At the height of his success in Boston in 1920, Charles A. Ponzi was hailed by those he was cheating as the greatest Italian who ever lived. “You’re wrong,” he said modestly, “there’s Columbus, who discovered America, and Marconi, who discovered radio.” “But, Charlie, you discovered money,” they told him.

(San Diego Daily Transcript – July 16, 1974)

I admit that it may sound a bit ludicrous, but lately I have been thinking on how to devise mathematical models of Ponzi schemes.

It is clear that a Ponzi scheme is unsustainable and that it will, sooner or later, collapse under its own weight. The scammer promoting such a scheme will be owing ever-increasing amounts of money to the investors, and as soon as the influx of cash is not enough to pay off the debts plus interest, the scheme will collapse.

[ Charles Ponzi in 1920 - photo courtesy of the U.S. government ]

Ponzi schemes have happened for a long time, but the scheme bears the name of its most “illustrious” scammer, Charles Ponzi (1882–1949) , who ran a huge fraudulent operation in the U.S. in 1919 and 1920.

Note that:

• the early investors in a Ponzi scheme will make money if they drop out before the whole thing collapses. On the other hand, the later investors will lose money.
• there’s a money transfer from the later investors to the scammer promoting the scheme and the earlier investors, so to say. As such, one has the incentive to be an early investor provided that the fraud lasts long enough for one to profit.
• an investor might be aware that there’s fraud going on and still invest if he thinks that the scheme will last a bit longer before it collapses so that he can get his money back and earn the interest.

How to devise mathematical models of Ponzi schemes? Which variables to choose? Which assumptions to make? It is not nearly as easy as one might think at first glance, I must say. An over-simplistic model is easy to devise, but it will tell us little. I have been building some models, and I will most likely write about them in future posts.