Optimal Auditing with Scoring: Theory and Application to Insurance Fraud

This article makes a bridge between the theory of optimal auditing and the scoring methodology in an asymmetric information setting. Our application is meant for asurance claims fraud, but it can be applied to many other activities that use the scoring approach. We show that the optimal auditing strategy takes the form of a "Red Flags Strategy" which consists in referring claims to a Special Investigative unit (SIU) when certain fraud indicators are observed. Fraud indicators are classified based on the degree to which they reveal an increasing probability of fraud. This strategy remains optimal even when the investigation policy is budget constrained. Moreover, the auditing policy acts as a deterrence device and we explain why it requires the commitment of the insurer and how it should affect the incentives of SIU staffs. the models is calibrated with data from a large European insurance company. We compute a critical suspicion index for fraud, providing a threshold above which all claims must be audited and we estimate the potential gain that could be derived from the optimal auditing policy. We show that it is possible to improve these results by separating different groups of insureds with different moral costs of fraud. Finally, our results indicate how the deterrence effect of the audit scheme can be taken into account and how it affects the optimal auditing strategy. Mots clés : Audit, scoring, Fraude à l'assurance, Stratégie d'indicateurs, Indicateurs de fraude, Indice de suspicion, Coût moral de la fraude, Effet de dissasion.