Threshold optimization of risk-based authentication under costly regulatory restrictions of PSD2

This paper addresses the problem of threshold decision optimization in risk-based authentication (RBA) systems under the value-based fraud rate constraints of PSD2. We propose a mathematical model for deciding whether to allow a transaction, require additional Strong Customer Authentication (SCA), or deny the transaction based on a risk score and transaction amount. We introduce constraints on the value-fraud-rate – the fraction of fraud by value among allowed transactions – in accordance with PSD2 thresholds (0.13%, 0.06%, 0.01%)[1][2]. An algorithm for tuning decision thresholds for each transaction amount range is developed, providing guarantees that fraud rates remain below the regulatory limits. A simulation experiment on a generated transaction dataset with risk scores and fraud labels is conducted. The results demonstrate that the proposed approach satisfies regulatory requirements (value-fraud-rate not exceeding 0.13%/0.06%/0.01% for the respective amount tiers) while allowing a significantly higher proportion of transactions to proceed without additional authentication compared to baseline strategies. We analyze how the threshold settings affect SCA trigger frequency and fraud levels, and discuss practical implications of deploying the proposed method in cloud-based banking and Payment Service Provider (PSP) platforms to support trusted transaction authentication.