On Thursday 12 January Ilya Muzykantskiy (Upper Sixth) gave a fun-packed and informative lecture on the mathematics underlying Ponzi Schemes, a financial scam involving dubious investment opportunities which promise more than they can deliver. The talk started with a brief history of these schemes tracing their origin back to Boston fraudster Charles Ponzi, before giving more detailed information about the scandal which shocked Wall Street in 2009, the collapse of Bernard Madoff’s hedge fund. This was the largest financial crime in history and resulted in a staggering loss of $65 billion, and an unprecedented 150 year jail sentence for Madoff, who personally embezzled an estimated $18 billion. Ilya outlined how both the naivety and greed of Madoff’s clients led to vital clues to the funds unviability being missed.

The main body of the talk however was a technical, Mathematical analysis of the evolution of Ponzi schemes which Ilya himself had developed. His model used standard assumptions taken from the insurance industry (maximization of log-utility) to predict the behaviour of individual investors, and then built differential equations to investigate the growth of the whole scheme, as both the underlying economy grew and as more people heard about the scheme.

Read the full report.