Bayesian multinomial latent variable modeling for fraud and abuse detection in health insurance

Healthcare fraud and abuse are a serious challenge to healthcare payers and to the entire society. This article presents a predictive model for fraud and abuse detection in health insurance based on a training dataset of manually reviewed claims. The goal of the analysis is to predict different fraud and abuse probabilities for new invoices. The prediction is based on a wide framework of fraud and abuse reports which examine the behavior of medical providers and insured members by measuring systematic deviation from usual patterns in medical claims data. We show that models which directly use the results of the reports as model covariates do not exploit the full potential in terms of predictive quality. Instead, we propose a multinomial Bayesian latent variable model which summarizes behavioral patterns in latent variables, and predicts different fraud and abuse probabilities. The estimation of model parameters is based on a Markov Chain Monte Carlo (MCMC) algorithm using Bayesian shrinkage techniques. The presented approach improves the identification of fraudulent and abusive claims compared to different benchmark approaches.     

Game theoretic modelling of service agent warranty fraud

When a warranty provider outsources warranty servicing to an external service agent this agent may act in a fraudulent manner. In this paper we consider a special case of service agent fraud—with the service agent overbilling the warranty provider for some of the warranty claims. A detailed inspection of a claim may be made to identify whether or not the service agent has committed fraud, but this inspection involves an additional cost to the warranty provider. This cost may be recovered by imposing a penalty on the service agent whenever a fraud is committed and it is detected. This penalty is specified in the maintenance service contract. A game theoretic approach is used to find the optimal overbilling strategy for the service agent and the optimal inspection strategy for the warranty provider. The optimal solution is the mixed strategy Nash equilibrium of a static game between the two parties.     

Sarmanov family of multivariate distributions for bivariate dynamic claim counts model

To predict future claims, it is well-known that the most recent claims are more predictive than older ones. However, classic panel data models for claim counts, such as the multivariate negative binomial distribution, do not put any time weight on past claims. More complex models can be used to consider this property, but often need numerical procedures to estimate parameters. When we want to add a dependence between different claim count types, the task would be even more difficult to handle. In this paper, we propose a bivariate dynamic model for claim counts, where past claims experience of a given claim type is used to better predict the other type of claims. This new bivariate dynamic distribution for claim counts is based on random effects that come from the Sarmanov family of multivariate distributions. To obtain a proper dynamic distribution based on this kind of bivariate priors, an approximation of the posterior distribution of the random effects is proposed. The resulting model can be seen as an extension of the dynamic heterogeneity model described in Bolancé et al. (2007). We apply this model to two samples of data from a major Canadian insurance company, where we show that the proposed model is one of the best models to adjust the data. We also show that the proposed model allows more flexibility in computing predictive premiums because closed-form expressions can be easily derived for the predictive distribution, the moments and the predictive moments.     

���ڱ�ֵCox���̵ĸ�������׼����ģ��

??Traditional claims reserve approaches are all based on aggregated data and usually produce inaccurate projections of the reserve because the aggregated data make a great loss of information contained in individual claims. Thus, the researcher in actuarial science developed the so-called individual claim models that are based on marked Poisson processes. However, due to the inappropriateness of Poisson distribution in modelling the claims distributions, the present paper propose marked Cox processes as reserve models. Compared with the aggregate claims models, the models proposed in the current paper take more sufficient use of information contained in data and can be expected to produce more accurate evaluations in claim loss reserving.     

A marked Cox model for the number of IBNR claims: Theory

Incurred but not reported (IBNR) loss reserving is an important issue for Property & Casualty (P&C) insurers. To calculate IBNR reserve, one needs to model claim arrivals and then predict IBNR claims. However, factors such as temporal dependence among claim arrivals and environmental variation are often not incorporated in many of the current loss reserving models, which may greatly affect the accuracy of IBNR predictions.In this paper, we propose to model the claim arrival process together with its reporting delays as a marked Cox process. Our model is versatile in modeling temporal dependence, allowing also for natural interpretations. This paper focuses mainly on the theoretical aspects of the proposed model. We show that the associated reported claim process and IBNR claim process are both marked Cox processes with easily convertible intensity functions and marking distributions. The proposed model can also account for fluctuations in the exposure. By an order statistics property, we show that the corresponding discretely observed process preserves all the information about the claim arrivals. Finally, we derive closed-form expressions for both the autocorrelation function (ACF) and the distributions of the numbers of reported claims and IBNR claims. Model estimation and its applications are considered in a subsequent paper, Badescu et al. (2015b).     

Predicting automobile claims bodily injury severity with sequential ordered logit models

Despite the large cost of bodily injury (BI) claims in motor insurance, relatively little research has been done in this area. Many companies estimate (and therefore reserve) bodily injury compensation directly from initial medical reports. This practice may underestimate the final cost, because the severity is often assessed during the recovery period. Since the evaluation of this severity is often only qualitative, in this paper we apply an ordered multiple choice model at different moments in the life of a claim reported to an insurance company. We assume that the information available to the insurer does not flow continuously, because it is obtained at different stages. Using a real data set, we show that the application of sequential ordered logit models leads to a significant improvement in the prediction of the BI severity level, compared to the subjective classification that is used in practice. We also show that these results could improve the insurer’s reserves notably.     

Support vector regression for warranty claim forecasting

Forecasting the number of warranty claims is vitally important for manufacturers/warranty providers in preparing fiscal plans. In existing literature, a number of techniques such as log-linear Poisson models, Kalman filter, time series models, and artificial neural network models have been developed. Nevertheless, one might find two weaknesses existing in these approaches: (1) they do not consider the fact that warranty claims reported in the recent months might be more important in forecasting future warranty claims than those reported in the earlier months, and (2) they are developed based on repair rates (i.e., the total number of claims divided by the total number of products in service), which can cause information loss through such an arithmetic-mean operation.To overcome the above two weaknesses, this paper introduces two different approaches to forecasting warranty claims: the first is a weighted support vector regression (SVR) model and the second is a weighted SVR-based time series model. These two approaches can be applied to two scenarios: when only claim rate data are available and when original claim data are available. Two case studies are conducted to validate the two modelling approaches. On the basis of model evaluation over six months ahead forecasting, the results show that the proposed models exhibit superior performance compared to that of multilayer perceptrons, radial basis function networks and ordinary support vector regression models.     

An analysis of voluntary recycled content claims under demand benefit and uncertain recycled input supply

We focus on the problem of choosing the optimal recycled content claim under stochastic local recycled content availability under two claim types — period specific (when claims have to hold each period) and average (when claims are evaluated across periods). We show conditions under which specific claims are higher than average claims, and explore cases where the optimal claims and profits are aligned to be in the same direction.     

A machine learning approach for individual claims reserving in insurance

Accurate loss reserves are an important item in the financial statement of an insurance company and are mostly evaluated by macrolevel models with aggregate data in run‐off triangles. In recent years, a new set of literature has considered individual claims data and proposed parametric reserving models based on claim history profiles. In this paper, we present a nonparametric and flexible approach for estimating outstanding liabilities using all the covariates associated to the policy, its policyholder, and all the information received by the insurance company on the individual claims since its reporting date. We develop a machine learning–based method and explain how to build specific subsets of data for the machine learning algorithms to be trained and assessed on. The choice for a nonparametric model leads to new issues since the target variables (claim occurrence and claim severity) are right‐censored most of the time. The performance of our approach is evaluated by comparing the predictive values of the reserve estimates with their true values on simulated data. We compare our individual approach with the most used aggregate data method, namely, chain ladder, with respect to the bias and the variance of the estimates. We also provide a short real case study based on a Dutch loan insurance portfolio.     

Risk aggregation based on the Poisson INAR(1) process with periodic structure

In this paper, we consider a risk model by introducing a temporal dependence between the claim numbers under periodic environment, which generalizes several discrete-time risk models. The model proposed is based on the Poisson INAR(1) process with periodic structure. We study the moment-generating function of the aggregate claims. The distribution of the aggregate claims is discussed when the individual claim size is exponentially distributed.     

Collective risk models with dependence

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such risk models in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.     

Universal contingent claims in a general market environment and multiplicative measures: Examples and applications

We present and further develop the concept of a universal contingent claim introduced by the author in 1995. This concept provides a unified framework for the analysis of a wide class of financial derivatives.A universal contingent claim describes the time evolution of a contingent payoff. In the simplest case of a European contingent claim, this time evolution is given by a family of nonnegative linear operators, the valuation operators. For more complex contingent claims, the time evolution that is given by the valuation operators can be interrupted by discrete or continuous activation of external influences that are described by, generally speaking, nonlinear operators, the activation operators. For example, Bermudan and American contingent claims represent discretely and continuously activated universal contingent claims with the activation operators being the nonlinear maximum operators.We show that the value of a universal contingent claim is given by a multiplicative measure introduced by the author in 1995. Roughly speaking, a multiplicative measure is an operator-valued (in general, an abstract measure with values in a partial monoid) function on a semiring of sets which is multiplicative on the union of disjoint sets. We also show that the value of a universal contingent claim is determined by a, generally speaking, impulsive semilinear evolution equation.     

On a risk model with claim investigation

In this paper, a queue-based claims investigation mechanism is considered to model an insurer’s claim processing practices. The resulting risk model may be viewed as a first step in developing models with more realistic claim investigation mechanisms. Related to claim investigations, claim settlement delays and time dependent payments have been studied in a ruin context by, e.g. Taylor (1979), Cai and Dickson (2002), and Trufin et al. (2011). However, little has been done on queue-based investigation mechanisms. We first demonstrate the impact of a particular claim investigation system on some common ruin-related quantities when claims arrive according to a compound Poisson process, and investigation times are of a combination of exponential form. Probabilistic interpretations for the defective renewal equation components are also provided. Finally, via numerical examples, we explore various risk management questions related to this problem such as how claim investigation strategies can help an insurer control its activities within its risk appetite.     

An individual loss reserving model with independent reporting and settlement

The main purpose of this paper is to assess and demonstrate the advantage of claims reserving models based on individual data in forecasting future liabilities over traditional models on aggregate data both theoretically and numerically. The available information consists of the reporting delays, settlement delays and claim payments. The model settings include Poisson distributed frequency of claims produced by each policy, claims payable at the settlement time, and the amount of payment depending only on its settlement delay. While such settings are applicable to certain but not all practical cases, the principal purpose of the paper is to examine the efficiency of individual data against aggregate data. We refer to loss reserving as to estimate the projections of the outstanding liabilities on observed information. The efficiency of the individual loss reserving against classical aggregate loss reservings, namely Chain-Ladder (C-L) and Bornhuetter–Ferguson (B–F), is assessed by comparing the asymptotic variances of the errors in estimating the conditional expectation (projection) of the outstanding liability between individual, C-L and B–F reservings. The research shows a significant increase in the accuracy of loss reserving by using individual data compared with aggregate data.     

Severity modeling of extreme insurance claims for tariffication

Generalized linear models are common instruments for the pricing of non-life insurance contracts. They are used to estimate the expected frequency and severity of insurance claims. However, these models do not work adequately for extreme claim sizes. To accommodate for these extreme claim sizes, we develop the threshold severity model, that splits the claim size distribution in areas below and above a given threshold. More specifically, the extreme insurance claims above the threshold are modeled in the sense of the peaks-over-threshold methodology from extreme value theory using the generalized Pareto distribution for the excess distribution, and the claims below the threshold are captured by a generalized linear model based on the truncated gamma distribution. Subsequently, we develop the corresponding concrete log-likelihood functions above and below the threshold. Moreover, in the presence of simulated extreme claim sizes following a log-normal as well as Burr Type XII distribution, we demonstrate the superiority of the threshold severity model compared to the commonly used generalized linear model based on the gamma distribution.     

Generalized linear models for dependent frequency and severity of insurance claims

Traditionally, claim counts and amounts are assumed to be independent in non-life insurance. This paper explores how this often unwarranted assumption can be relaxed in a simple way while incorporating rating factors into the model. The approach consists of fitting generalized linear models to the marginal frequency and the conditional severity components of the total claim cost; dependence between them is induced by treating the number of claims as a covariate in the model for the average claim size. In addition to being easy to implement, this modeling strategy has the advantage that when Poisson counts are assumed together with a log-link for the conditional severity model, the resulting pure premium is the product of a marginal mean frequency, a modified marginal mean severity, and an easily interpreted correction term that reflects the dependence. The approach is illustrated through simulations and applied to a Canadian automobile insurance dataset.     

An application of time series methods to financial guarantee insurance

This article comprises a summary of a study made in Finland concerning solvency issues in financial guarantee insurance. The time fluctuation of bankruptcy intensity is analyzed by fitting Box-Jenkins type models to empirical data, and this fluctuation is combined with the variation in the number of claims and the individual claim sizes, based on empirical claim size distribution. The estimated models are used to evaluate, for example, the variance of the claims ratio and of the solvency ratio of the financial guarantee insurer. The variation range of the solvency ratio and the appropriate premium level are discussed with numerical examples.     

The benefit to consumers from generic scoring models based on credit reports

Received on 1 July 1991. The benefit to consumers from the use of informative creditreports is demonstrated by showing the improvement in creditdecisions when generic scoring models based on credit reportsare implemented. If these models are highly predictive, thenthe truncation of credit reports will reduce the predictivepower of bureau-based generic scoring systems. As a result,more good credit risks will be denied credit, and more poorcredit risks will be granted credit. It is shown that, evenwhen applied to credit applications that had already been screenedand approved, the use of generic scoring models significantlyimproves credit grantors' ability to predict and eliminate bankruptcies,charge-offs, and delinquencies. As applied to existing accounts,bureau-based generic scores are shown to have predictive valuefor at least 3 months, while scores 12 months old may not bevery powerful. Even though bureau-based scores shift towardsthe high-risk end of the distribution during a recession, theycontinue to rank risk very well. When coupled with application-basedcredit-scoring models, scores based on credit-bureau data furtherimprove the predictive power of the model-the improvements beinggreater with more complete bureau information. We conclude thatgovernment-imposed limits on credit information are anti-consumerby fostering more errors in credit decisions.     

Probabilistic models for medical insurance claims

The paper develops two probabilistic models for claim size in health insurance based on the claims of families and individuals covered by the policy. First, general models for the numbers of families and persons covered by a medical insurance are developed. These are then used to construct models for claim size. Applications of these general models are then analysed and discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Semiparametric model for prediction of individual claim loss reserving

The estimation of loss reserves for incurred but not reported (IBNR) claims presents an important task for insurance companies to predict their liabilities. Conventional methods, such as ladder or separation methods based on aggregated or grouped claims of the so-called “run-off triangle”, have been illustrated to have some drawbacks. Recently, individual claim loss models have attracted a great deal of interest in actuarial literature, which can overcome the shortcomings of aggregated claim loss models. In this paper, we propose an alternative individual claim loss model, which has a semiparametric structure and can be used to fit flexibly the claim loss reserving. Local likelihood is employed to estimate the parametric and nonparametric components of the model, and their asymptotic properties are discussed. Then the prediction of the IBNR claim loss reserving is investigated. A simulation study is carried out to evaluate the performance of the proposed methods.