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The Ponzi Scheme Puzzle
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The PGBM model for a couple of counteracting, exponentially growing capital flows is presented: the available capital stock $X(t)$ evolves according to a variant of inhomogeneous geometric Brownian motion (GBM) with time-dependent drift, in particular, to the stochastic differential equation $dX(t)=[pX(t)+\rho_1\exp(q_1 t)+\rho_2\exp(q_2 t)]dt+\sigma X(t) dW(t)$, where $W(t)$ is a Wiener process. As a paragon, we study a continuous-time model for a nine-parameter Ponzi scheme with an exponentially growing number of investors. Investors either maintain their investment or withdraw it after some fixed investment span and quit the system. The first two moments of the process and hence a closed-form solution for the mean path are given. The capital stock exhibits a dynamic lognormal probability distribution as long as the system remains solvent. The assumed stochastic performance allows for earlier or later collaps of the investment system as compared to the deterministic analogy ($\sig.
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Lecture Notes in Computer Science
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Bernie Madoff perpetrated the largest Ponzi scheme in American history, by utilizing a fraud methodology that dates back to the mid 1800s. Madoff was able to steal roughly $65 billion dollars, during the course of multiple decades. Due to the elaborate nature of the fraud and the reputable public perception of Madoff, the scheme not only went uncovered after multiple Securities and Exchange Commission (SEC) tips and pre-investigations, but also continued to grow and increase in popularity, among investors worldwide. The SEC conducted haphazard investigations and utilized inexperienced examiners that lacked support and guidance from senior leaders. The SEC also had understaffed personnel, which kept overworked investigators from thoroughly examining Madoff's network. In this research paper, the author provides a critical analysis of the entire incident and also broadens the discussion to capture lessons learned, while extrapolating the details to consider fraud prevention techniques that can be used by organizations of all sizes, in multiple industries. The author offers recommendations to investors to reduce the potential of falling victim to future Ponzi schemes and/or other fraudulent behavior in corporate settings. The research includes recommendations for investigators so they are prepared to quickly discover and eliminate Ponzi schemes and other fraudulent activities, while mitigating losses. Lastly, insight into the reform and modifications that have occurred within the SEC as a result of the Madoff Ponzi scheme will be reviewed.
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