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.     

Das Dreiecksverhältnis zwischen Versicherer,Versicherungsnehmer und versicherten Personen in Innenhaftungsfällen der D&;O-Versicherung

The article deals with the rights and obligations between the policyholder, the insured directors and officers of the policyholder and the insurer in ‘Insured vs. Insured’ D&;O claims. Based on a case study where several directors commit wrongful acts the following questions will be examined: (1) whether or not the policyholder is entitled to directly claim damages from the insurer, (2) whether or not the policyholder violates its duties towards the insurer or the insured directors by its deliberate choice not to make claims against all insured at the same time but in different policy periods, and (3) which obligations has the policyholder towards its directors when there is not sufficient coverage to cover all claims of the policyholder against the directors.     

A Statistical Basis for Claims Experience Monitoring

Abstract

By claims experience monitoring is meant the systematic comparison of the forecasts from a claims model with claims experience as it emerges subsequently. In the event that the stochastic properties of the forecasts are known, the comparison can be represented as a collection of probabilistic statements. This is stochastic monitoring. This paper defines this process rigorously in terms of statistical hypothesis testing. If the model is a regression model (which is the case for most stochastic claims models), then the natural form of hypothesis test is a number of likelihood ratio tests, one for each parameter in the valuation model. Such testing is shown to be very easily implemented by means of generalized linear modeling software. This tests the formal structure of the claims model and is referred to as microtesting. There may be other quantities (e.g., amount of claim payments in a defined interval) that require testing for practical reasons. This sort of testing is referred to as macrotesting, and its formulation is also discussed.     

Beyond accounting and back: An empirical examination of the relative relevance of earnings and “other” information

Ohlson (1995) models firm value as a function of book value, earnings, and analysts' earnings forecasts which capture “other” information not yet reflected in the financial statements. Within this framework, stock returns reflect information from earnings and forecasts, each of which is different in terms of reliability and timeliness. For the period 1984–2012, this paper examines time trends and the influence of aggregate market conditions on the relative relevance of earnings and forecasts. In this context, relative relevance is defined as the incremental explanatory power of earnings or forecasts, relative to their combined explanatory power with respect to the cross-section of stock returns. This inquiry is motivated by anecdotal evidence and recent research, which suggests that aggregate market conditions influence the usefulness of accounting information for investors. The findings show that while the relative relevance of earnings has remained stable, the relative relevance of forecasts has increased over time. I also find that the relative relevance of earnings is higher in bad years, i.e. years with low market returns or elevated market uncertainty. Overall, the results reported in this study suggest that despite the increase in the relevance of timely “other” information, investors tend to rely more on reliable accounting information during bad years.     

A data set for modeling claims processes—TSA claims data

This data insight highlights the Transportation Security Administration (TSA) claims data as an underused data set that would be particularly useful to researchers developing statistical models to analyze claim frequency and severity. Individuals who have been injured or had items damaged, lost or stolen may make a claim for losses to the TSA. The federal government reports information on every claim from 2002 to 2017 at https://www.dhs.gov/tsa-claims-data . Information collected includes claim date and type and site as well as closed claim amount and disposition (whether it was approved in full, denied, or settled. We provide summary statistics on the frequency and the severity of the data for the years 2003 to 2015. The data set has several unique features including severity is not truncated (there is no deductible), there are significant mass points in the severity data, and the frequency data shows a high degree of auto correlation if compiled on a weekly basis, and substantial frequency mass points at zero for daily data.     

A Parimutuel Market Microstructure for Contingent Claims

Parimutuel principles are widely used as an alternative to fixed odds gambling in which a bookmaker acts as a dealer by quoting fixed rates of return on specified wagers. A parimutuel game is conducted as a call auction in which odds are allowed to fluctuate during the betting period until the betting period is closed or the auction ‘called’. The prices or odds of wagers are set based upon the relative amounts wagered on each risky outcome. In financial microstructure terms, trading under parimutuel principles is characterised by (1) call auction, non‐continuous trading; (2) riskless funding of claim payouts using the amounts paid for all of the claims during the auction; (3) special equilibrium pricing conditions requiring the relative prices of contingent claims equal the relative aggregate amounts wagered on such claims; (4) endogenous determination of unique state prices; and (5) higher efficiency. Recently, a number of large investment banks have adopted a parimutuel mechanism for offering contingent claims on various economic indices, such as the US Nonfarm payroll report and Eurozone Harmonised inflation. Our paper shows how the market microstructure incorporating parimutuel principles for contingent claims which allows for notional transactions, limit orders, and bundling of claims across states is constructed. We prove the existence of a unique price equilibrium for such a market and suggest an algorithm for computing the equilibrium. We also suggest that for a broad class of contingent claims, that the parimutuel microstructure recently deployed offers many advantages over the dominant dealer and exchange continuous time mechanisms.     

Time-variation in term premia: International survey-based evidence

Using a large, previously unexplored data set of survey-based interest rate forecasts that covers a broad range of countries, this paper re-examines the expectations hypothesis of the term structure of interest rates. We find that survey-based interest rate forecasts outperform not only a random walk forecast, but also outperform forecasts from forward rates. When using these superior survey-based forecasts in a modified expectations hypothesis test, the expectations hypothesis is rejected for fewer countries, at lower significance levels, and has greater explanatory power than when using a traditional forward rates-based test. We furthermore document strong time-variation in the term premia, which is an important reason why the traditional expectations hypothesis test is rejected so frequently. This time-variation seems to arise from the changing attitudes towards risk among market participants and as a compensation for the change in liquidity in the term structure. Finally, we find that generalizing findings from earlier U.S. studies to other countries may lead to bias in the true economic relationships in these countries.     

Recursions and fast Fourier transforms for a new bivariate aggregate claims model

Insurance companies typically face multiple sources (types) of claims. Therefore, modelling dependencies among different types of risks is extremely important for evaluating the aggregate claims of an insurer. In this paper, we first introduce a multivariate aggregate claims model, which allows dependencies among claim numbers as well as dependencies among claim sizes. For this proposed model, we derive recursive formulas for the joint probability functions of different types of claims. In addition, we extend the concept of exponential tilting to the multivariate fast Fourier transform and use it to compute the joint probability functions of the various types of claims. We provide numerical examples to compare the accuracy and efficiency of the two computation methods.     

Ordering the largest claim amounts and ranges from two sets of heterogeneous portfolios

This paper investigates the ordering properties of the largest claim amounts and sample ranges arising from two sets of heterogeneous portfolios. First, some sufficient conditions are provided in the sense of the usual stochastic ordering to compare the largest claim amounts from two sets of independent or interdependent claims. Second, comparison results on the largest claim amounts in the sense of the reversed hazard rate and hazard rate orderings are established for two batches of heterogeneous independent claims. Finally, we present sufficient conditions to stochastically compare sample ranges from two sets of heterogeneous claims by means of the usual stochastic ordering. Some numerical examples are also given to illustrate the theoretical findings. The results established here not only extend and generalize those known in the literature, but also provide insight that will be useful to lay down the annual premiums of policyholders.     

Incentive Conflicts,Bundling Claims,and the Interaction among Financial Claimants

We show that for certain capital structures equity has an incentive to buy out another claim and alter the firm's investment strategy so as to maximize the combined value of equity and the acquired claim. This restructuring may reintroduce agency problems into capital structures which appear to avoid agency conflicts. By bundling claims, it is possible to avoid this agency problem. The agency problem is also eliminated by dispersed ownership of the claims.     

Are Auditors Professionally Skeptical? Evidence from Auditors’ Going‐Concern Opinions and Management Earnings Forecasts

We examine whether auditors exercise professional skepticism about management earnings forecasts when making going‐concern decisions. Using publicly issued management earnings forecasts as a proxy for earnings forecasts provided by managers to auditors, we find that management earnings forecasts are negatively associated with both auditors’ going‐concern opinions and subsequent bankruptcy. The weight auditors put on management forecasts in the going‐concern decision is not significantly different from the weight implied in the bankruptcy prediction model. Moreover, compared with the bankruptcy model, auditors assign a lower weight to management forecasts they perceive as being less credible, including those (1) issued by managers who issued optimistic forecasts in the previous two years, and (2) predicting high earnings increases or high earnings. Taken together, our evidence is consistent with auditors being professionally skeptical about management earnings forecasts when making going‐concern decisions.     

“扭亏”公司业绩预告的“变脸”研究

本文利用单变量对比和多元Logit回归分析扭亏公司业绩预告变脸的原因。基于2002-2008年的大样本研究表明,预测难度是影响变脸概率的重要因素。具体表现在,当年中报或季报已实现扭亏的样本在预告中变脸的可能性显著低于其他样本;以微利扭亏的样本更有可能变脸;盈利持续性比较低的样本变脸的可能性比较高。另外,审计师规模或公司规模比较大的样本变脸的可能性比较低。这些研究结果有助于投资者和监管部门深入了解上市公司的业绩预告披露行为。     

The effect of non-audit services on client risk, acceptance and staffing decisions

The Sarbanes Oxley Act of 2002 prohibited auditing firms from providing certain non-audit services to audit clients and left open the possibility that other currently non-prohibited services could also be banned. This prohibition hinges, in part, on regulatory concerns that auditors were willing to accept prospective higher risk clients in order to obtain more profitable non-audit service engagements. Accounting firms rejected this claim. Given the prospect that more non-audit services could be prohibited, we revisit this debate by examining these competing claims in an experiment in which we manipulate risk and the potential to sell non-audit services and then observe the impact of these variables on auditors’ client acceptance and subsequent staffing decisions. Specifically, audit partners received client information and were asked to make an acceptance decision and propose a staffing plan for a potential engagement. We find that a higher (lower) level of risk decreased (increased) the likelihood of acceptance and this relation did not vary with the potential to provide non-audit services. These results do not support the regulators’ claims but are consistent with the firms’ claims. Further, we found that more experienced auditors were assigned to the prospective client whose management had lower integrity. This staffing plan is consistent with a risk adaptation strategy for the client with lower integrity. The prohibition of certain non-audit services has been justified on the grounds that auditors might engage in systematic opportunistic behavior. However, our results do not find such behavior which should inform the current PCAOB deliberation over whether additional services should be banned. Alternatively, different justification must be found for the prohibitions.     

Attainability of European path-independent claims in incomplete markets

In this paper we consider the question which path-independent claims are attainable through self-financing trading strategies in an incomplete market. For continuous-time stochastic volatility models we show that only affine payoffs can be replicated. We provide a simple proof for this proposition based on the requirement that, for replication, the stock and the claim must be locally perfectly correlated, and based on the partial differential equation that any path-independent claim has to satisfy. Moreover, we show that this result does not carry over to discrete setups.     

Mean and dispersion modelling for policy claims costs

A model for the statistical analysis of the total amount of insurance paid out on a policy is developed and applied. The model simultaneously deals with the number of claims (zero or more) and the amount of each claim. The number of claims is from a Poisson-based discrete distribution. Individual claim sizes are from a continuous right skewed distribution. The resulting distribution of total claim size is a mixed discrete-continuous model, with positive probability of a zero claim. The means and dispersions of the claim frequency and claim size distribution are modeled in terms of risk factors. The model is applied to a car insurance data set.     

超预期股本扩张与分析师每股盈余预测

卖方分析师的每股盈余预测在实证文献中被广泛使用。该指标同时依赖于分析师对目标公司未来净利润的预测和对目标公司未来股本数量的预测。因此,如果在分析师发布预测后,目标公司的股本数量发生超出分析师预期的扩张,则每股盈余预测将无法代表分析师对目标公司未来基本面的预测。本文构建了“调整后每股盈余预测”指标,该指标可剔除超预期股本扩张对每股盈余预测的影响,真实反映分析师对目标公司未来基本面的预测。本文应用该指标,在两个具体的实证研究场景中证明了,忽略超预期股本扩张的影响可能得出错误的实证结论。本文还进一步指出了三个忽略超预期股本扩张的影响可能导致错误实证结果的研究场景。     

超预期股本扩张与分析师每股盈余预测

卖方分析师的每股盈余预测在实证文献中被广泛使用。该指标同时依赖于分析师对目标公司未来净利润的预测和对目标公司未来股本数量的预测。因此,如果在分析师发布预测后,目标公司的股本数量发生超出分析师预期的扩张,则每股盈余预测将无法代表分析师对目标公司未来基本面的预测。本文构建了“调整后每股盈余预测”指标,该指标可剔除超预期股本扩张对每股盈余预测的影响,真实反映分析师对目标公司未来基本面的预测。本文应用该指标,在两个具体的实证研究场景中证明了,忽略超预期股本扩张的影响可能得出错误的实证结论。本文还进一步指出了三个忽略超预期股本扩张的影响可能导致错误实证结果的研究场景。     

Momentum and default risk. Some results using the jump component

In this paper we separate the total stock return into its continuous and jump component to test whether stock return predictability should be attributed to omitted risk factors or behavioral finance theories. We extend results from the US market to the Spanish stock market, which, despite being a developed market, presents several differences in terms of stock characteristics, financial system, investor typology and cultural dimensions. The results show that the jump component has significant explanatory power for the premium of three characteristics (size, book-to-market and illiquidity), which is at odds with risk-based explanations. Using the same testing strategy, we try to shed some light on an important controversy concerning the relationship between default risk and momentum. The results suggest that default risk is not the source of momentum returns.     

Forecasting Beta: How Well Does the 'Five-Year Rule of Thumb' Do?

CAPM betas are generally estimated from historical data and applied to a future period. There is widespread evidence that the CAPM betas vary considerably over time and this raises two questions: can this variation be explained and can it be forecast better than the 'five-year rule of thumb' (i.e using the most recently estimated beta)? We estimate time-varying betas and explain the time-variation in the betas using regression models which we subsequently use for forecasting. We find that forecasting equations have good explanatory power but that their forecasts are dominated, on average, by the five-year rule of thumb.