We demonstrate the use of Adaptive Stress Testing to detect and address potential vulnerabilities in a financial environment. We develop a simplified model for credit card fraud detection that utilizes a linear regression classifier based on historical payment transaction data coupled with business rules. We then apply the reinforcement learning model known as Adaptive Stress Testing to train an agent, that can be thought of as a potential fraudster, to find the most likely path to system failure -- successfully defrauding the system. We show the connection between this most likely failure path and the limits of the classifier and discuss how the fraud detection system's business rules can be further augmented to mitigate these failure modes.