What question did this study set out to answer?

To develop a finite-population model for evaluating fraud risk in batch escrow processing transactions.

February 12, 20260 citationsOpen Access

Finite Population Fraud Risk in Batch Escrow Processing

Key Points

To develop a finite-population model for evaluating fraud risk in batch escrow processing transactions.
Modeling a batch of N transactions with K fraudulent trades using hypergeometric distribution
Deriving expressions for various risk metrics like incident probability and expected safe run length
Formulating an optimal stopping problem to balance throughput and expected loss
Validating results with Monte Carlo simulations
Closed-form expressions for fraud encounter distribution, including pmf, survival function, and hazard rate
Insights into operational risk metrics like expected safe run length and incident probability
Optimal stopping policy defined by a monotone threshold based on marginal conditions
Validation of theoretical results through Monte Carlo simulations against standard baselines

Abstract

I develop an exact finite-population model for fraud exposure in batch escrow processing. Modeling a batch of N transactions with exactly K fraudulent trades processed sequentially in a hypergeometric environment, I derive closed-form expressions for the distribution of the first fraud encounter, including the pmf, survival function, hazard rate, expectation, and variance. These results yield interpretable operational risk metrics such as incident probablity after processing m transactions, expected safe run length, and quantile-based checkpoints. I further formulate and solve an optimal stopping problem that balances throughput against expected loss, showing that the optimal policy is a montone trhreshold characterized by a one-step marginal condition. Monte Carlo simulations validate the theoretical results and compare the derived policies to standard baselines.

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