1. Richard A. Derrig Ph. D. OPAL Consulting LLC Visiting Scholar, Wharton School University of Pennsylvania Fraud Fighting Actuaries Mathematical Models for Insurance Fraud Detection (HANDOUT) CAS Predictive Modeling October 4-5, 2004

2. FRAUD DEFINITION Principles  Clear and willful act  Proscribed by law  Obtaining money or value  Under false pretenses Abuse/ Ethical Lapse: Fails one or more Principles

3. HOW MUCH FRAUD?

4. AIB FRAUD INDICATORS W Accident Characteristics (19) uNo report by police officer at scene uNo witnesses to accident W Claimant Characteristics (11) uRetained an attorney very quickly uHad a history of previous claims W Insured Driver Characteristics (8) uHad a history of previous claims uGave address as hotel or P.O. Box 1989 Examples

5. AIB FRAUD INDICATORS W Injury Characteristics (12) uInjury consisted of strain/sprain only uNo objective evidence of injury W Treatment Characteristics (9) uLarge number of visits to a chiropractor uDC provided 3 or more modalities on most visits W Lost Wages Characteristics (6) uClaimant worked for self or family member uEmployer wage differs from claimed wage loss 1989 Examples

6. Easy Paid Investigation Routine Adjusting DM Target Claims Investigative Paid Build-up Negotiation Civil Proceeding Suspected Fraud SIU Criminal Referral Prosecuted Not Guilty Guilty

7. DM Databases Scoring Functions Graded Output Non-Suspicious Claims Routine Claims Suspicious Claims Complicated Claims

8. Fraud Detection Plan Fraud Detection Plan W STEP 1:SAMPLE W STEP 2:FEATURES W STEP 3:FEATURE SELECTION W STEP 4:CLUSTER W STEP 5:ASSESSMENT W STEP 6:MODEL W STEP7:STATIC TESTING W STEP 8:DYNAMIC TESTING: Real time operation of acceptable model, record outcomes, repeat steps 1-7 as needed to fine tune model and parameters.

9. POTENTIAL VALUE OF AN ARTIFICIAL INTELLIGENCE SCORING SYSTEM W Screening to Detect Fraud Early W Auditing of Closed Claims to Measure Fraud W Sorting to Select Efficiently among Special Investigative Unit Referrals W Providing Evidence to Support a Denial W Protecting against Bad-Faith

10. Using Kohonen’s Self-Organizing Feature Map to Uncover Automobile Bodily Injury Claims Fraud PATRICK L. BROCKETT Gus S. Wortham Chaired Prof. of Risk Management University of Texas at Austin XIAOHUA XIA University of Texas, at Austin RICHARD A. DERRIG Senior Vice President Automobile Insurers Bureau of Massachusetts Vice President of Research Insurance Fraud Bureau of Massachusetts JOURNAL OF RISK AND INSURANCE, 65:2, 245-274, 1998,

11. MAPPING: PATTERNS-TO-UNITS Patterns

12. Modeling Hidden Exposures in Claim Severity via the EM Algorithm Grzegorz A. Rempala Department of Mathematics University of Louisville and Richard A. Derrig OPAL Consulting LLC & Wharton School, University of Pennsylvania

13. Figure 2: EM Fit Left panel: mixture of normal distributions fitted via the EM algorithm to BI data Right panel: Three normal components of the mixture. Source: Modeling Hidden Exposures in Claim Severity via the EM Algorithm, Grzegorz A. Rempala, Richard A. Derrig, pg. 13, 11/18/02

14. Fraud Classification Using Principal Component Analysis of RIDITs PATRICK L. BROCKETT Gus S. Wortham Chaired Prof. of Risk Management University of Texas at Austin RICHARD A. DERRIG Senior Vice President Automobile Insurers Bureau of Massachusetts Vice President of Research Insurance Fraud Bureau of Massachusetts LINDA L. GOLDEN Marlene & Morton Meyerson Centennial Professor in Business University of Texas Austin, Texas ARNOLD LEVINE Professor Emeritus Department of Mathematics Tulane University New Orleans LA MARK ALPERT Professor of Marketing University of Texas Austin, Texas JOURNAL OF RISK AND INSURANCE, 69:3, SEPT. 2002

15. TABLE 1 Computation of PRIDIT Scores Variable Label Proportion of “Yes” B t1 ("Yes") B t2 (“No") Large # of Visits to ChiropractorTRT144%-.56.44 Chiropractor provided 3 or more modalities on most visits TRT212%-.88.12 Large # of visits to a physical therapistTRT38%-.92.08 MRI or CT scan but no inpatient hospital charges TRT420%-.80.20 Use of “high volume” medical providerTRT531%-.69.31 Significant gaps in course of treatmentTRT69%-.91.09 Treatment was unusually prolonged (> 6 months) TRT724%-.76.24 Indep. Medical examiner questioned extent of treatment TRT811%-.89.11 Medical audit raised questions about charges TRT94%-.96.04

16. TABLE 2 Weights for Treatment Variables Variable PRIDIT Weights W (∞) Regression Weights TRT1.30.32*** TRT2.19.19*** TRT3.53.22*** TRT4.38.07 TRT5.02.08* TRT6.70-.01 TRT7.82.03 TRT8.37.18*** TRT9-.13.24** Regression significance shown at 1% (***), 5% (**) or 10% (*) levels.

17. TABLE 3 PRIDIT Transformed Indicators, Scores and Classes ClaimTRT 1 TRT 2 TRT 3 TRT 4 TRT 5 TRT 6 TRT 7 TRT 8 TRT 9 ScoreClass 1 0.440.120.080.20.310.090.240.110.04.072 2 0.440.120.080.2-0.690.090.240.110.04.072 3 0.44-0.88-0.920.20.31-0.91-0.760.110.04-.251 4 -0.560.120.080.20.310.090.240.110.04.042 5 -0.56-0.880.080.20.310.090.240.110.04.022 6 0.440.120.080.20.310.090.240.110.04.072 7 -0.560.120.080.20.310.09-0.76-0.890.04-.101 8 -0.440.120.080.2-0.690.090.240.110.04.022 9 -0.56-0.880.08-0.80.310.090.240.11-0.96.052 10 -0.560.120.080.20.310.090.240.110.04.042

18. TABLE 7 AIB Fraud and Suspicion Score Data Top 10 Fraud Indicators by Weight PRIDITAdj. Reg. ScoreInv. Reg. Score ACC3ACC1ACC11 ACC4ACC9CLT4 ACC15ACC10CLT7 CLT11ACC19CLT11 INJ1CLT11INJ1 INJ2INS6INJ3 INJ5INJ2INJ8 INJ6INJ9INJ11 INS8TRT1 LW6TRT9

19. TABLE 10 AIB Fraud Indicator and Suspicious Score Classes Fraud/Non-fraud Classifications PRIDIT Fraud Non- fraudAll Adjuster Regression Score Fraud30535 Non- Fraud 326092 All6265127 (  =11.3) [4.0, 31.8]

20. The BI Settlement Process and Structure of Negotiated Payments Richard A. Derrig Automobile Insurers Bureau of MA Herbert I. Weisberg Correlation Research Inc. NBER Insurance Group Meeting Cambridge, Massachusetts February 6-7, 2004

21. BI Negotiation Leverage Points AdjusterAttorney/Claimant Ability to go to TrialAbility to Build-Up Company has the Settlement FundsAsymmetric Information on Accident, Injury, and Treatment Attorney, Medical Provider, or Claimant needs Money No Cooperation for IME, Sworn or Recorded Statements Necessary without Trial History of Prior Settlements by Claim Type History of Prior Settlements by Claim Type (with Attorney) Settlement Delay by InvestigationCompany Investigation Costs Settlement Authorization Process in Company Unfair Claim Practices (93A) Initial Determination of LiabilityAdjuster Need to Close Files

23. IME Savings PIP & BI PIP Sample:1996 CSE Net Savings (PIP)-0.8% Savings from IME Requ but not Comp0.7% Savings from Positive IMEs-0.4% Cost of Negative IMEs-1.1% PIP+BI Sample:1996 CSE Net Savings (PIP+BI)8.7% Savings from IME Requ but not Comp*4.3% Savings from Positive IMEs4.9% Cost of Negative IMEs-0.5% *Inclusion of All PIP claims with IME requested but not completed. 4.2% of savings for 1993 AIB comes from PIPs with no matching BIs where IME requested but not completed. 2.1% savings for 1996 DCD. 2.7% savings for 1996 CSE.

24. Net IME Savings By Suspicion Level ClaimIMESuspicion Level PaymentTypeClaimsNone (0) Low (1-3) Mod (4-6) High (7-10) ALL PIP Suspicion Score (CSE Model) PIP PIP & BI matching -8.1%-2.9%3.4%-1.6%-0.8% BI Suspicion Score (NHR Model) PIP+BIBestPIP & BI matching -8.0%0.5%14.4%-4.5%6.2%

25. Settlement Ratios by Injury and Suspicion VariablePIP Suspicion Score = Low (0-3) PIP Suspicion Score = Mod to High (4-10) PIP Suspicion Score = All 1996 (N-336)1996 (N-216)1996 (N-552) Str/SPAll OtherStr/SPAll OtherStr/SPAll Other Settlement 81%19%94%6%86%14% Avg. Settlement/Specials Ratio 3.013.812.583.612.823.77 Median Settlement/Specials Ratio 2.692.892.402.572.552.89

26. Evaluation Variables Prior Tobit Model (1993AY) W Claimed Medicals (+) W Claimed Wages (+) W Fault (+) W Attorney (+18%) W Fracture (+82%) W Serious Visible Injury at Scene (+36%) W Disability Weeks (+10% @ 3 weeks) New Model Additions (1996AY) W Non-Emergency CT/MRI (+31%) W Low Impact Collision (-14%) W Three Claimants in Vehicle (-12%) W Same BI + PIP Co. (-10%) [Passengers -22%]

27. Negotiation Variables New Model Additions (1996AY) W Atty (1st) Demand Ratio to Specials (+8% @ 6 X Specials) W BI IME No Show (-30%) W BI IME Positive Outcome (-15%) W BI Ten Point Suspicion Score (-12% @ 5.0 Average) W [1993 Build-up Variable (-10%)] W Unknown Disability (+53%) W [93A (Bad Faith) Letter Not Significant] W [In Suit Not Significant] W [SIU Referral (-6%) but Not Significant] W [EUO Not Significant] Note: PIP IME No Show also significantly reduces BI + PIP by discouraging BI claim altogether (-3%).

28. Total Value of Negotiation Variables Total Compensation VariablesAvg. Claim/Factor Evaluation Variables$13,948 Disability Unknown1.05 1 st Demand Ratio1.09 BI IME No Show0.99 BI IME Not Requested0.90 BI IME Performed with Positive Outcome0.97 Suspicion0.87 Negotiation Variables0.87 Total Compensation Model Payment$12,058 Actual Total Compensation$11,863 Actual BI Payment$8,551

30. INSURANCE FRAUD RESEARCH REGISTER (IFRR) W Annotated Bibliography of Insurance Fraud Research Worldwide. W Available www.derrig.com or www.ifb.orgwww.derrig.com www.ifb.org W 160 Participants W 360 References to Published Research and Working Papers W Join, It’s Free!

31. REFERENCES Brockett, Patrick L., Derrig, Richard A., Golden, Linda L., Levine, Albert and Alpert, Mark, (2002), Fraud Classification Using Principal Component Analysis of RIDITs, Journal of Risk and Insurance, 69:3, 341-373. Brockett, Patrick L., Xiaohua, Xia and Derrig, Richard A., (1998), Using Kohonen’ Self-Organizing Feature Map to Uncover Automobile Bodily Injury Claims Fraud, Journal of Risk and Insurance, 65:245-274 Derrig, R.A. and H.I. Weisberg, [2004], Determinants of Total Compensation for Auto Bodily Injury Liability Under No-Fault: Investigation, Negotiation and the Suspicion of Fraud, ”, Insurance and Risk Management, Volume 71, (4), pp. 633-662. Derrig, R.A., H.I. Weisberg and Xiu Chen, [1994], Behavioral Factors and Lotteries Under No-Fault with a Monetary Threshold: A Study of Massachusetts Automobile Claims, Journal of Risk and Insurance, 61:2, 245-275. Derrig, Richard A. and Ostaszewski, Krzysztof M., (1995), Fuzzy Techniques of Pattern Recognition in Risk and Claim Classification, Journal of Risk and Insurance, 62:447-482 Viaene, Stijn, Derrig, Richard A., Baesens, Bart, and Dedene, Guido, (2002), A Comparison of State-of-the-Art Classification Techniques for Expert Automobile Insurance Fraud Detection, Journal of Risk and Insurance, 69:3, 373-423.