The Zero-Inflated Cure Rate Regression Model: Applications to Fraud Detection in Bank Loan Portfolios

Abstract

In this paper, we introduce a methodology based on the zero-inflated cure rate model to detect fraudsters in bank loan applications. Our approach enables us to accommodate three different types of loan applicants, i.e., fraudsters, those who are susceptible to default and finally, those who are not susceptible to default. An advantage of our approach is to accommodate zero-inflated times, which is not possible in the standard cure rate model. To illustrate the proposed method, a real dataset of loan survival times is fitted by the zeroinflated Weibull cure rate model. The parameter estimation is reached by maximum likelihood estimation procedure and Monte Carlo simulations are carried out to check its finite sample performance.Thus, the analysed dataset here is comprised by customers who, in one way or another, have not honoured their contractual obligations with the bank, either by fraud in the application process, or by loss of creditworthiness over time, along with good clients who honour their obligations and have never experienced the event of default.According to the aforementioned scenario, and bringing to the statistical terminology, the dataset of study in this paper comprises three different types of non-negative survival times: survival times starting in zero for fraudsters, positive default times for delinquents, and the absence of registration, or censored time, for non-defaulting clients. These considerations delimit the data we will cover in this paper: a set of zeros, positives and unrecorded (censored) banking loan survival times. Such data must be addressed to make a holistic risk management of the loan portfolio, that is, dealing with fraud prevention, delinquency control and ensure the customer loyalty growth.For using survival analysis techniques, we must consider the modelling outcome of interest be the survival time after loan concession, also mentioned as customer or loan survival time, which is represented by time to occurrence of the event of default. This has been done in different papers, such as [1,2,3,22]. The reason for the increased use of survival analysis in credit risk over other modelling techniques, besides allowing monitor over time the credit risk of the loan portfolio, is that it can accommodate censored data, which are not supported, for example, in credit scoring techniques based purely on good and bad client classification, see for instance [11,13,21].Notwithstanding, survival analysis deals with non-negative and censored data, however, generally without excess, or even, the presence of zeros. Unlike survival data analysis, in other areas we can observe most commonly the existence of non-negative data with the presence of zeros, sometimes with excess, usually in count data analysis, see for example [4,8,10,12,16]. Therefore, it is already a commonplace the expression "zero-inflated data".Perhaps it is unhelpful, or cruelly insensitive, if we consider human survival times equal to zero in clinical trials and medical studies. Hence, it might be why, to the best of our know...

The Zero-Inflated Promotion Cure Rate Regression Model Applied to Fraud Propensity in Bank Loan Applications

“…In this case, we can see that x has three levels, referring to a particular characteristics of a bank's customer profile. Note that, it is slightly different than one presented in [4], p. 14 , because it is a sample extracted randomly from the database provided by the bank. The following are two applications, the first related to the proposed model by 15, and the second, for comparison purposes, referring to the proposed model by Louzada et al [4].…”

“…To accommodate zero excess in a survival analysis of loan portfolios, in [4], the authors have proposed a modification in the survival function of the cure rate model, which has led to the improper survival function given in 4, also labelled as zero-inflated cure rate model. In this scenario, information from fraudsters in loan applications is exploited through the joint modelling of the survival time of fraudsters, which is equal to zero, along with the survival times of the remaining portfolio.…”

“…The purpose of this article is to follow the method as done in [4], and then propose a way of incorporating the fraction of zeros into the biological based model of Chen et al [3]. The advantage of incorporating the fraction of zeros in this model is that the model enables us to interpret the underlying causes that lead to occurrence of default so that we can compare if customers at higher risk of default are also more likely to commit fraud in credit applications.…”

“…To accommodate the presence of zeros, which is impossible in the cure rate model shown above, Louzada et al [4] proposed a zero-inflated cure rate model, which survival function is given by:…”