Ponzi system dynamics: time to bankruptcy, optimal bailout time and a condition for survival
Bibliographic record
Abstract
Every Ponzi ‘investment’ scheme is fraudulent and it is destined for eventual collapse. When a Ponzi scheme starts, the early investors make unreasonably high profits from receiving unrealistically high (and ‘guaranteed’) returns. However, unbeknown to the unsuspecting investors, these returns are made possible not by the profits of a successful business (as claimed by the Ponzi operator), but by the deposits of the later investors. Unfortunately for the later investors, either the money runs out, or the operator disappears. In this paper we analyse the time-dependent progress of the Ponzi scheme using a system of two difference (and later, differential) equations. We estimate the time to bankruptcy (and optimal bailout time for the operator) under several assumptions, including constant, time-varying, random deposit amounts by the investors. An optimal control model to maximise the final time cash balance is also included. We provide a simple (but unusual) condition under which the Ponzi scheme may never go bankrupt. Our results could be of potential benefit to investors to warn them not to be fooled by the promises of a Ponzi scheme fraudster; and if they have invested in such a scheme, to cash out before the scheme collapses or the promoter disappears.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.015 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".