Statistics and Its Interface

Volume 6 (2013)

Number 1

Collusion set detection using a quasi hidden Markov model

Pages: 53 – 64



Xiaoyu Wu (United Oversea Bank, Singapore)

Zhengxiao Wu (Department of Statistics and Applied Probability, National University of Singapore)


In the stock market, a collusion set is defined as a group of individuals or organizations who act cooperatively with an intention of manipulating security price. Collusion-based malpractices impose large costs on the economy, but few techniques have yet been developed for collusion set detection. In this article, we propose a quasi hidden Markov model (QHMM) approach. In particular, we consider the transactions as a marked point process with hidden states, and we calculate the class conditional probabilities to identify the malicious transactions. The detection algorithms associated with the model are recursive, hence suitable for online monitoring and detection. The QHMM approach has several advantages over the existent methods. For example, it incorporates the transaction times into the model naturally, and the model parameters can be estimated from the data systematically. We illustrate the models with examples and the QHMM performs well in our numerical experiments.


collusion set, fraud detection, hidden Markov model, quasi-hidden Markov model

2010 Mathematics Subject Classification

Primary 60K35, 62Mxx. Secondary 62Pxx.

Published 18 March 2013