Fraud Fighting Actuaries
Mathematical Models for
Insurance Fraud Detection
(HANDOUT)
Richard A. Derrig Ph. D.
OPAL Consulting LLC
Visiting Scholar, Wharton School
University of Pennsylvania
CAS Predictive Modeling
October 4-5, 2004
FRAUD DEFINITION
Principles
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Clear and willful act
Proscribed by law
Obtaining money or value
Under false pretenses
Abuse/ Ethical Lapse: Fails one or more Principles
HOW MUCH FRAUD?
Table 1
1989 Bodily Injury Liability Claim Sample
"Fraud Definition"
1. Apparent Fraud or Build-up
Approximate Claim
Count Percentage
43.80%
2. Apparent Fraud Only
3. Apparent Fraud Referable for
Criminal Investigation
9.10%
1.00%
4. IFB Referrals Qualifying for
Active Investigation
0.50%
5. IFB Investigations Referable
to Prosecution
0.10%
6. Prosecution Successes
0.09%
Source: AIB Studies of 1989 BI Claims; RAD estimates of IFB Data
AIB FRAUD INDICATORS
1989 Examples

Accident Characteristics (19)
No report by police officer at scene
No witnesses to accident

Claimant Characteristics (11)
Retained an attorney very quickly
Had a history of previous claims

Insured Driver Characteristics (8)
Had a history of previous claims
Gave address as hotel or P.O. Box
AIB FRAUD INDICATORS
1989 Examples



Injury Characteristics (12)
Injury consisted of strain/sprain only
No objective evidence of injury
Treatment Characteristics (9)
Large number of visits to a chiropractor
DC provided 3 or more modalities on most visits
Lost Wages Characteristics (6)
Claimant worked for self or family member
Employer wage differs from claimed wage loss
Target Claims
DM
Easy
Paid
Routine Adjusting
Investigation
Investigative Paid
Suspected
Fraud SIU
Build-up
Negotiation
Civil
Proceeding
Not Guilty
Criminal
Referral
Prosecuted
Guilty
DM
Databases
Scoring Functions
Graded Output
Non-Suspicious Claims
Routine Claims
Suspicious Claims
Complicated Claims
Fraud Detection Plan
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STEP 1:SAMPLE
STEP 2:FEATURES
STEP 3:FEATURE SELECTION
STEP 4:CLUSTER
STEP 5:ASSESSMENT
STEP 6:MODEL
STEP7:STATIC TESTING
STEP 8:DYNAMIC TESTING: Real time
operation of acceptable model, record
outcomes, repeat steps 1-7 as needed to fine
tune model and parameters.
POTENTIAL VALUE OF AN ARTIFICIAL
INTELLIGENCE SCORING SYSTEM
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Screening to Detect Fraud Early
Auditing of Closed Claims to Measure
Fraud
Sorting to Select Efficiently among
Special Investigative Unit Referrals
Providing Evidence to Support a Denial
Protecting against Bad-Faith
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,
Patterns
MAPPING: PATTERNS-TO-UNITS
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
Figure 2: EM Fit
Left panel: mixture of normal distributions fitted
via the EM algorithm to BI data
Source: Modeling Hidden Exposures in Claim Severity via the EM Algorithm,
Grzegorz A. Rempala, Richard A. Derrig, pg. 13, 11/18/02
Right panel: Three normal components of the
mixture.
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
TABLE 1
Computation of PRIDIT Scores
Variable
Proportion of B
t1
“Yes”
Label
("Yes")
Variable
Bt2
(“No")
Large # of Visits to Chiropractor
TRT1
44%
-.56
.44
Chiropractor provided 3 or more
modalities on most visits
TRT2
12%
-.88
.12
Large # of visits to a physical therapist
TRT3
8%
-.92
.08
MRI or CT scan but no inpatient
hospital charges
TRT4
20%
-.80
.20
Use of “high volume” medical provider
TRT5
31%
-.69
.31
Significant gaps in course of treatment
TRT6
9%
-.91
.09
Treatment was unusually prolonged
(> 6 months)
TRT7
24%
-.76
.24
Indep. Medical examiner questioned
extent of treatment
TRT8
11%
-.89
.11
Medical audit raised questions about
charges
TRT9
4%
-.96
.04
TABLE 2
Weights for Treatment Variables
PRIDIT Weights
W(∞)
Regression
Weights
TRT1
.30
.32***
TRT2
.19
.19***
TRT3
.53
.22***
TRT4
TRT5
.38
.02
.07
.08*
TRT6
TRT7
TRT8
.70
.82
.37
-.01
.03
.18***
Variable
TRT9
-.13
.24**
Regression significance shown at 1% (***), 5% (**) or 10% (*)
levels.
TABLE 3
PRIDIT Transformed Indicators, Scores and Classes
Claim
TRT
1
TRT
2
TRT
3
TRT
4
TRT
5
TRT
6
TRT
7
TRT
8
TRT
9
Score
Class
1
0.44
0.12
0.08
0.2
0.31
0.09
0.24
0.11
0.04
.07
2
2
0.44
0.12
0.08
0.2
-0.69
0.09
0.24
0.11
0.04
.07
2
3
0.44
-0.88
-0.92
0.2
0.31
-0.91
-0.76
0.11
0.04
-.25
1
4
-0.56
0.12
0.08
0.2
0.31
0.09
0.24
0.11
0.04
.04
2
5
-0.56
-0.88
0.08
0.2
0.31
0.09
0.24
0.11
0.04
.02
2
6
0.44
0.12
0.08
0.2
0.31
0.09
0.24
0.11
0.04
.07
2
7
-0.56
0.12
0.08
0.2
0.31
0.09
-0.76
-0.89
0.04
-.10
1
8
-0.44
0.12
0.08
0.2
-0.69
0.09
0.24
0.11
0.04
.02
2
9
-0.56
-0.88
0.08
-0.8
0.31
0.09
0.24
0.11
-0.96
.05
2
10
-0.56
0.12
0.08
0.2
0.31
0.09
0.24
0.11
0.04
.04
2
TABLE 7
AIB Fraud and Suspicion Score Data
Top 10 Fraud Indicators by Weight
PRIDIT
ACC3
Adj. Reg. Score
ACC1
Inv. Reg. Score
ACC11
ACC4
ACC15
CLT11
ACC9
ACC10
ACC19
CLT4
CLT7
CLT11
INJ1
INJ2
CLT11
INS6
INJ1
INJ3
INJ5
INJ2
INJ8
INJ6
INS8
TRT1
INJ9
TRT1
LW6
INJ11
TRT1
TRT9
TABLE 10
AIB Fraud Indicator and
Suspicious Score Classes
Fraud/Non-fraud Classifications
PRIDIT
Adjuster
Regression
Score
Fraud
Nonfraud
All
Fraud
30
5
35
NonFraud
All
32
60
92
62
65
127
( =11.3) [4.0, 31.8]
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
BI Negotiation Leverage Points
Adjuster
Attorney/Claimant
Ability to go to Trial
Ability to Build-Up
Company has the Settlement Funds
Asymmetric 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 Investigation
Company Investigation Costs
Settlement Authorization Process in
Company
Unfair Claim Practices (93A)
Initial Determination of Liability
Adjuster Need to Close Files
Figure 8-3
1996 Settlement/Specials Ratio Distribution
20.00%
18.00%
16.00%
14.00%
% of Claims
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
0 to 0.5
0.5 to 1
1 to 1.5
1.5 to 2
2 to 2.5
2.5 to 3
3 to 3.5
3.5 to 4
4 to 4.5
4.5 to 5
5 to 5.5
5.5 to 6
6 to 6.5
6.5 to 7
Settlement/Specials Ratio
7 to 7.5
7.5 to 8
8 to 8.5
8.5 to 9
9 to 9.5 9.5 to 10 10 to 20 20 to 30
IME Savings PIP & BI
PIP
Sample:
Net Savings (PIP)
1996 CSE
-0.8%
Savings from IME Requ but not Comp
0.7%
Savings from Positive IMEs
-0.4%
Cost of Negative IMEs
-1.1%
PIP+BI
Sample:
Net Savings (PIP+BI)
1996 CSE
8.7%
Savings from IME Requ but not Comp*
4.3%
Savings from Positive IMEs
4.9%
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.
Net IME Savings By Suspicion Level
Claim
IME
Payment Type
Suspicion Level
Claims
None Low
(0)
(1-3)
Mod
(4-6)
High
(7-10)
ALL
PIP Suspicion Score (CSE Model)
PIP
PIP
PIP & BI
matching
-8.1%
-2.9%
3.4%
-1.6%
-0.8%
BI Suspicion Score (NHR Model)
PIP+BI
Best
PIP & BI
matching
-8.0%
0.5%
14.4%
-4.5%
6.2%
Settlement Ratios by Injury and Suspicion
Variable
PIP 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/SP
All Other
Settlement
Str/SP
All Other
Settlement
Str/SP
All
Other
Settlement
81%
19%
94%
6%
86%
14%
Avg.
Settlement/Specials
Ratio
3.01
3.81
2.58
3.61
2.82
3.77
Median
Settlement/Specials
Ratio
2.69
2.89
2.40
2.57
2.55
2.89
Evaluation Variables
Prior Tobit Model (1993AY)
 Claimed Medicals (+)
 Claimed Wages (+)
 Fault (+)
 Attorney (+18%)
 Fracture (+82%)
 Serious Visible Injury at Scene (+36%)
 Disability Weeks (+10% @ 3 weeks)
New Model Additions (1996AY)
 Non-Emergency CT/MRI (+31%)
 Low Impact Collision (-14%)
 Three Claimants in Vehicle (-12%)
 Same BI + PIP Co. (-10%) [Passengers -22%]
Negotiation Variables
New Model Additions (1996AY)
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Atty (1st) Demand Ratio to Specials (+8% @ 6 X Specials)
BI IME No Show (-30%)
BI IME Positive Outcome (-15%)
BI Ten Point Suspicion Score (-12% @ 5.0 Average)
[1993 Build-up Variable (-10%)]
Unknown Disability (+53%)
[93A (Bad Faith) Letter Not Significant]
[In Suit Not Significant]
[SIU Referral (-6%) but Not Significant]
[EUO Not Significant]
Note: PIP IME No Show also significantly reduces BI + PIP by
discouraging BI claim altogether (-3%).
Total Value of Negotiation Variables
Total Compensation Variables
Avg. Claim/Factor
Evaluation Variables
$13,948
Disability Unknown
1.05
1st Demand Ratio
1.09
BI IME No Show
0.99
BI IME Not Requested
0.90
BI IME Performed with Positive Outcome
0.97
Suspicion
0.87
Negotiation Variables
0.87
Total Compensation Model Payment
$12,058
Actual Total Compensation
$11,863
Actual BI Payment
$8,551
INSURANCE FRAUD RESEARCH
REGISTER (IFRR)
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
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Fraud Research Worldwide.
Available www.derrig.com or
www.ifb.org
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360 References to Published Research
and Working Papers
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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.