Claims Auditing in Automobile Insurance: Fraud Detection and Deterrence Objectives

Research on insurer management of opportunism in claiming has developed in two parallel literatures. One is a theoretical literature on insurance contracting that yields predictions about the nature of optimal auditing strategies for the deterrence of fraud. The other is a literature based upon statistical analysis of claims that yields empirical strategies for the detection of fraudulent claims. This article links the two literatures by providing an empirical assessment of insurers’ auditing practices in relation to theoretical predictions. The analysis makes use of a data set on the disposition of more than 1,000 randomly selected automobile personal injury protection claims settled in the state of Massachusetts. The findings of the article are consistent with the use of rational auditing strategies by insurers and with the use of audits for both deterrence and detection.     

Assessing Consumer Fraud Risk in Insurance Claims

Abstract

We present an unsupervised learning method for classifying consumer insurance claims according to their suspiciousness of fraud versus nonfraud. The predictor variables contained within a claim file that are used in this analysis can be binary, ordinal categorical, or continuous variates. They are constructed such that the ordinal position of the response to the predictor variable bears a monotonic relationship with the fraud suspicion of the claim. Thus, although no individual variable is of itself assumed to be determinative of fraud, each of the individual variables gives a “hint” or indication as to the suspiciousness of fraud for the overall claim file. The presented method statistically concatenates the totality of these “hints” to make an overall assessment of the ranking of fraud risk for the claim files without using any a priori fraud-classified or -labeled subset of data. We first present a scoring method for the predictor variables that puts all the variables (whether binary “red flag indicators,” ordinal categorical variables with different categories of possible response values, or continuous variables) onto a common –1 to 1 scale for comparison and further use. This allows us to aggregate variables with disparate numbers of potential values. We next show how to concatenate the individual variables and obtain a measure of variable worth for fraud detection, and then how to obtain an overall holistic claim file suspicion value capable of being used to rank the claim files for determining which claims to pay and the order in which to investigate claims further for fraud. The proposed method provides three useful outputs not usually available with other unsupervised methods: (1) an ordinal measure of overall claim file fraud suspicion level, (2) a measure of the importance of each individual predictor variable in determining the overall suspicion levels of claims, and (3) a classification function capable of being applied to existing claims as well as new incoming claims. The overall claim file score is also available to be correlated with exogenous variables such as claimant demographics or highvolume physician or lawyer involvement. We illustrate that the incorporation of continuous variables in their continuous form helps classification and that the method has internal and external validity via empirical analysis of real data sets. A detailed application to automobile bodily injury fraud detection is presented.     

A Comparison of State-of-the-Art Classification Techniques for Expert Automobile Insurance Claim Fraud Detection

Several state‐of‐the‐art binary classification techniques are experimentally evaluated in the context of expert automobile insurance claim fraud detection. The predictive power of logistic regression, C4.5 decision tree, k‐nearest neighbor, Bayesian learning multilayer perceptron neural network, least‐squares support vector machine, naive Bayes, and tree‐augmented naive Bayes classification is contrasted. For most of these algorithm types, we report on several operationalizations using alternative hyperparameter or design choices. We compare these in terms of mean percentage correctly classified (PCC) and mean area under the receiver operating characteristic (AUROC) curve using a stratified, blocked, ten‐fold cross‐validation experiment. We also contrast algorithm type performance visually by means of the convex hull of the receiver operating characteristic (ROC) curves associated with the alternative operationalizations per algorithm type. The study is based on a data set of 1,399 personal injury protection claims from 1993 accidents collected by the Automobile Insurers Bureau of Massachusetts. To stay as close to real‐life operating conditions as possible, we consider only predictors that are known relatively early in the life of a claim. Furthermore, based on the qualification of each available claim by both a verbal expert assessment of suspicion of fraud and a ten‐point‐scale expert suspicion score, we can compare classification for different target/class encoding schemes. Finally, we also investigate the added value of systematically collecting nonflag predictors for suspicion of fraud modeling purposes. From the observed results, we may state that: (1) independent of the target encoding scheme and the algorithm type, the inclusion of nonflag predictors allows us to significantly boost predictive performance; (2) for all the evaluated scenarios, the performance difference in terms of mean PCC and mean AUROC between many algorithm type operationalizations turns out to be rather small; visual comparison of the algorithm type ROC curve convex hulls also shows limited difference in performance over the range of operating conditions; (3) relatively simple and efficient techniques such as linear logistic regression and linear kernel least‐squares support vector machine classification show excellent overall predictive capabilities, and (smoothed) naive Bayes also performs well; and (4) the C4.5 decision tree operationalization results are rather disappointing; none of the tree operationalizations are capable of attaining mean AUROC performance in line with the best. Visual inspection of the evaluated scenarios reveals that the C4.5 algorithm type ROC curve convex hull is often dominated in large part by most of the other algorithm type hulls.     

The Impact of Insurance Fraud Detection Systems

This article analyzes the impact of detection systems in an insurance fraud context. In a noncommitment Costly State Verification setting insurers can only detect fraudulent claims by performing costly audits, and policyholders are overcompensated by the optimal insurance contract. We show that auditing becomes more effective and overcompensation can be reduced, when insurers are able to condition their audits on the information provided by detection systems.     

The Valuation of Multivariate Contingent Claims in Discrete Time Models

There are several examples in the literature of contingent claims whose payoffs depend on the outcomes of two or more stochastic variables. Familiar cases of such claims include options on a portfolio of options, options whose exercise price is stochastic, and options to exchange one asset for another. This paper derives risk neutral valuation relationships (RNVRs) in a discrete time setting that facilitate the pricing of such complex contingent claims in two specific cases: joint lognormally distributed underlying variables and constant proportional risk aversion on the part of investors, and joint normally distributed underlying variables and constant absolute risk aversion preferences, respectively. This methodology is then applied to the valuation of several interesting complex contingent claims such as multiperiod bonds, multicurrency option bonds, and investment options.     

Bagging集成方法在保险欺诈识别中的应用研究

保险欺诈不仅危及保险公司的正常经营,增加投保人的负担,甚至有可能影响到国家的金融稳定。随着大数据时代的到来,保险反欺诈亟需引入革命性技术。Bagging集成方法以其可调节模型结构、易于部署、参数空间可控、支持并行运算等特点成为保险公司进行保险反欺诈一个好的选择。Bagging方法主要包括Bagging算法、Random Subspace算法、Random Patches算法,它们又能与不同基学习器结合构成新的分支算法及算法特例。本文基于这些算法对保险欺诈问题进行了实证检验,分析了各算法及与基学习器的适用性问题,以及基学习器个数对算法表现的影响。分析发现:针对保险欺诈识别问题,在Bagging、Random Subspace、Random Patches三者之中,Random Patches算法的表现最好,Bagging的运行时间最短;不同算法适用的基学习器不同,但总体来说最适合Bagging集成方法的是决策树;基于决策树的方法都一致选择是否委托律师代理作为最重要的特征;基学习器个数对不同Bagging算法表现的影响并不一致。     

Deterring Fraud: The Role of General Damage Awards in Automobile Insurance Settlements

Awards for pain and suffering and other noneconomic losses account for over half of all damages awarded under third‐party auto insurance bodily injury settlements. This article hypothesizes that third‐party insurers use general damage awards to reduce the incentive to submit exaggerated claims for specific damages for injuries and lost wages. Consistent with this hypothesis, the article finds evidence using data on over 17,000 closed bodily injury claims that special damage claims that exceed their expected value receive proportionally lower general damage awards than claims that do not. Among the implications of this research is the possibility that insurers will be less zealous in challenging fraudulent special damage claims under a third‐party insurance regime than they will be under a first‐party insurance regime in which access to general damages is limited.     

The Impact of Rate Regulation on Claims: Evidence From Massachusetts Automobile Insurance

The article tests the hypothesis that insurance price subsidies created by rate regulation lead to higher insurance cost growth. The article makes use of data from the Massachusetts private passenger automobile insurance market, where cross‐subsidies were explicitly built into the rate structure through rules that limit rate differentials and differences in rate increases across driver rating categories. Two approaches are taken to study the potential loss cost reaction to the Massachusetts cross‐subsidies. The first approach compares Massachusetts with all other states while controlling for demographic, regulatory, and liability coverage levels. Loss cost levels that were about 29 percent above the expected level are found for Massachusetts during years 1978–1998, when premiums charged were those fixed by the state and included explicit subsidies for high‐risk drivers. A second approach considers changing cost levels across Massachusetts by studying loss cost changes by town and relating those changes to subsidy providers and subsidy receivers. Subsidy data based on accident year data for 1993–2004 show a significant and positive (relative) growth in loss costs and an increasing proportion of high‐risk drivers for towns that were subsidy receivers, in line with the theory of underlying incentives for adverse selection and moral hazard.     

汽车保险精算定价模型研究综述

汽车保险定价模型在非寿险精算领域内占有重要地位,本文对车险定价模型一百多年来的研究进展作了综述性的回顾。首先,本文介绍了车险定价模型的先验估费方法;其次着重介绍了时齐的后验估费方法,以及时变的先验后验相结合的精算模型;最后提出了车险定价模型的未来发展方向。     

Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models

Using the statistical methodology of semi-parametric regression and its connection with mixed models, this article revisits smoothing models for loss reserving and credibility. Apart from the flexibility inherent to all semiparametric methods, advantages of the semiparametric approach developed here are threefold. First, a Bayesian implementation of these smoothing models is relatively straightforward and allows simulation from the full predictive distribution of quantities of interest. Second, because the constructed models have an interpretation as (generalized) linear mixed models ((G)LMMs), standard statistical theory and software for (G)LMMs can be used. Third, more complicated data sets, dealing, for example, with quarterly development in a reserving context, heavy tails, semi-continuous data, or extensive longitudinal data, can be modeled within this framework.     

Fraud Detection Using a Multinomial Logit Model With Missing Information

Recently, Artís, Ayuso, and Guillén (2002, Journal of Risk and Insurance 69: 325–340; henceforth AAG) estimate a logit model using claims data. Some of the claims are categorized as “honest” and other claims are known to be fraudulent. Using the approach of Hausman, Abrevaya, and Scott‐Morton (1998 Journal of Econometrics 87: 239‐269), AAG estimate a modified logit model allowing for the possibility that some claims classified as honest might actually be fraudulent. Applying this model to data on Spanish automobile insurance claims, AGG find that 5 percent of the fraudulent claims go undetected. The purpose of this article is to estimate the model of AAG using a logit model with missing information. A constrained version of this model is used to reexamine the Spanish insurance claim data. The results indicate how to identify misclassified claims. We also show how misclassified claims can be identified using the AAG approach. We show that both approaches can be used to probabilistically identify misclassified claims.     

Expiration Dates in Automobile Insurance Contracts: The Curious Case of Last Policy Month Claims in Taiwan

This paper investigates a widespread trend in the Taiwanese automobile insurance market in which the loss claims of vehicle damage insurance contracts have a high propensity to occur just before the end of the policy year (as opposed to calendar year). We show that certain uncommon characteristics of claim data are consistently observed in the last policy month. We indirectly show that there is a severe time-varying excess claim problem in this market. The major sources of excess claims can be explained by the bonus-malus system problem and the auto-dealer incentive issue.     

Selection Bias and Auditing Policies for Insurance Claims

Selection bias results from a discrepancy between the range of estimation of a statistical model and its range of application. This is the case for fraud risk models, which are estimated on audited claims but applied on incoming claims in the design of auditing strategies. Now audited claims are a minority within the parent sample since they are chosen after a severe selection performed by claims adjusters. This article presents a statistical approach that counteracts selection bias without using a random auditing strategy. A two‐equation model on audit and fraud (a bivariate probit model with censoring) is estimated on a sample of claims where the experts are left free to take the audit decision. The expected overestimation of fraud risk derived from a single‐equation model is corrected. Results are close to those obtained with a random auditing strategy, at the expense of some instability with respect to the regression components set. Then we compare auditing policies derived from the different approaches.     

保险诈骗的成因、类型与防范

随着保险业的迅猛发展,保险诈骗案件也日渐增多。保险欺诈不仅给保险业造成巨额经济损失,损害了诚实投保人的利益．而且严重扰乱保险市场秩序,破坏了社会的稳定。应采取积极的防范措施,通过提高员工的综合素质、建立重大赔案调查制度、实现伤者医疗跟踪服务和实行保险行业信息共享等方式,减少保险骗赔案件的发生。     

The Role of Repetition and Observability in Deterring Insurance Fraud

In this paper, I analyze an inspection game between an insurer and an infinite sequence of policyholders, who can try to misrepresent relevant information in order to obtain coverage or lower insurance premium. Because claim-auditing is costly for the insurer, ex-post moral hazard problem arises. I find that the repeated game effect serves as a commitment device, allowing the insurer to deter fraud completely (for sufficiently high discount rate) but only when the policyholders observe past auditing strategies. Under weaker observability conditions, only partial efficiency gains are generally possible. I conclude that the insurers should spend resources on signaling their anti-fraud attempts to the potential policyholders. Similar conclusions can be drawn with respect to conceptually similar problems, such as tax evasion.