The Economics of Insurance Fraud Investigation:
Evidence of a Nash Equilibrium
Stephen P. D’Arcy, FCAS
University of Illinois
Richard A. Derrig Ph.D.
OPAL Consulting LLC
Herbert I. Weisberg
Correlation Research Inc.
NBER Presentation - February 2005
Outline
• Research Questions
• Automobile Bodily Injury Coverage and Claim Investigation
• Notation
• Nash Equilibrium Tables
• Results
Research Questions
What are the incentives for fraud investigation under the current market structure of automobile insurance in the United States?
What happens when different companies are responsible for paying different parts of a bodily injury claim?
Coverage for Automobile Bodily Injury Claims
• First Party Coverages– Medical Payments
– Personal Injury Protection (No-Fault)
• Third Party Coverages– Bodily Injury (BI) Liability
– Uninsured Motorist (UM)
• Subrogation• Our Example is No-Fault PIP and BI
Claim Investigation Tactics
• Independent Medical Exams (IME)
• Medical Audit (MA)
• Special Investigative Unit (SIU)
• Tracked Since 1995 in Massachusetts
• Tracked in Recent 2004 IRC Study of Auto Injury Claims countrywide
NotationCost of claim without any investigation:
PIP claim = Pi,j (i company has PIP, j company has Liability)
Liability claim (excess of PIP) = Li,j
Savings from investigations:
Savings on PIP claims = SP
Savings on Liability claims = SL
Savings on Total claim = ST
Level of investigation:
No investigation = 0
Optimal investigation based on PIP claims = A
Optimal investigation based on total claims = B
Investigation cost:
Cost of an A level investigation = IA
Cost of an B level investigation = IB
Claims
$
Total Saving
PIP Saving
Cost of Investigation
A B
STB
STA
SPBIB
SPA
IA
Figure 1Optimal Level of Claim Investigation
Table 1Single Insurer Case
Net Cost of Claim and Investigations
Level of Claim Investigation
None (0) PIP Based (A) Total Claim Based (B)
1,11,10,1 LPP 1101111101
111101
,,,,,
,,,
IAIASLASPASPA
LPP
1101111101
111101
,,,,,
,,,
IBIBSLBSPBSPB
LPP
Insurer 1 Level of Claim Investigation
None (0) PIP Based (A) Total Claim Based (B)
0
11 ,, LP
22 ,, LP
,,
,,,
111
111
IASLA
SPALP
2122 ,,, SLALP
,,
,,,
111
111
IBSLB
SPBLP
2122 ,,, SLBLP
A
1211 ,,, SLALP
,,,
,,
2222
22
IASLASPA
LP
,,
,,,
11
111
IASLA
SPALP
,,,
,,
222
22
IASLASPA
LP
,,
,,,,
112
11111
IBSLA
SLBSPBLP
,,,
,,,
22221
222
IASLASLB
SPALP
Insu
rer
2 L
evel
of
Inv
esti
gati
on
B
1211 ,,, SLBLP
,,,
,,
2222
22
IBSLBSPB
LP
,,
,,,,
112
11111
IASLB
SLASPALP
,,,
,,,
22212
222
IBSLBSLA
SPBLP
,,
,,,
11
111
IBSLB
SPBLP
,,,
,,
222
22
IBSLBSPB
LP
Table 2 -Two Insurer CaseNet Cost of Claim and Investigations (No Subrogation )
Table 4-Two Insurer CaseNet Cost of Claim and Investigations (Subrogation)
Insurer 1 Level of Claim Investigation
None (0) PIP Based (A) Total Claim Based (B)
0
1211121101 ,,,,, LLPPP
2221222102 ,,,,, LLPPP
,11,11,1
0,11,21,11,21,10,1
IASLASPA
SPALLPPP
2,12,12,22,1
2,22,10,2
SLASPALL
PPP
,11,11,1
0,11,21,11,21,10,1
IBSLBSPB
SPBLLPPP
2,12,12,22,1
2,22,10,2
SLBSPBLL
PPP
A
1,21,2
1,21,11,21,10,1
SLASPA
LLPPP
,22,22,2
0,22,22,1
2,22,10,2
IASLASPA
SPALL
PPP
,11,21,11,2
1,10,11,21,11,21,10,1
IASLASLASPA
SPASPALLPPP
,22,22,12,2
2,10,22,22,1
2,22,10,2
IASLASLASPA
SPASPALL
PPP
,11,21,11,2
1,10,11,21,11,21,10,1
IBSLASLBSPA
SPBSPBLLPPP
,22,22,12,2
2,10,22,22,1
2,22,10,2
IASLASLBSPA
SPBSPALL
PPP
Insu
rer 2
Lev
el o
f Cla
im In
vest
igat
ion
B
12121211121101 ,,,,,,, SLBSPBLLPPP
,,,,
,,,,,
2222202
2221222102
IBSLBSPBSPB
LLPPP
,11,21,11,2
1,10,11,21,11,21,10,1
IASLBSLASPB
SPASPALLPPP
,22,22,12,2
2,10,22,22,1
2,22,10,2
IBSLBSLASPB
SPASPBLL
PPP
,11,1,
0,11,21,11,21,10,1
IBSLBSPB
SPBLLPPP
,22,2,0,2
2,22,12,22,10,2
IBSLBSPBSPB
LLPPP
Massachusetts Experience I
• No-Fault State
• PIP Coverage of $8000
– Medical expenses
– Loss of income
– Other services and expenses
• Tort Threshold of $2000 in medical expenses
• Study of claim investigations
– IME costs ≈ SPA (PIP savings)
– Implies investigations consider total savings
– Total costs reduced net of cost by investigation
Massachusetts Experience II
• PIP and BI Company Same For Only 20% PIP Claims; Two companies 80% of Claims, a Non-Cooperative Game
• BI Coverage of $20,000 Compulsory; $100,000 Commonly Purchased
– Medical & Income expenses excess of PIP
– General Damages “Pain and Suffering”
– Attorney Fees for Claimant & Company
• Study of Claim Investigation: Claim Screen Experiment on 1996 Claims:
Four Companies tracked “Fraud Indicators” for each PIP Claim for six months; BI claim matched from database and both coded for relevant data (medicals, providers, injuries, suspicion (automated), investigation, attorney involvement, other data)
1993 Claim Sample and 1996 Population of Detailed Claim Database
DMFraud Indicators
Scoring Functions
Graded Output
Non-Suspicious ClaimsRoutine Claims
Suspicious ClaimsComplicated Claims
Massachusetts Experience III
• IME Savings Net of Cost ($350, $75 no show)• PIP Only: 0.1% All; 1.6% No Shows; Suspicion:
Moderate 2.6%; High -13.8%, None -3.4%• PIP & BI: 8.7% All; 4.3% No Shows; Suspicion:
Moderate 14.4%; High -4.5%, None -8.0%• Study Conclusion: Claim Scoring for Suspicion
Helps Maximize Savings Net of Cost by Reducing the Number of Claims Investigated without Savings
Claims
$
Total Saving
PIP Saving
Cost of Investigation
A B
STB
STA
SPBIB
SPA
IA
Figure 2Claim Investigation in Massachusetts
MA
Conclusion
• When viewed in non-cooperative game theoretic framework, insurers have liability reimbursement incentives to under investigate suspicious claims but Massachusetts data points to over investigation.
• Intelligent claim sorting creates more incentive (more $ available) to investigate for fraud and could move toward Nash equilibrium.
• Market structure revisions could increase fraud detection and reduce insurance costs
Summary of Tabular ResultsPIP
Sample: 1993 AIB 1996 DCD 1996 CSE
Net Savings (PIP)
Savings from IME Req but not Completed
Savings from Positive IMEs
Cost of Negative IMEs
0.2%
0.7%
0.7%
-1.3%
-0.2%
0.3%
0.4%
-0.9%
-0.2%
0.4%
0.2%
-0.8%
BI + PIP
Sample: 1993 AIB 1996 DCD 1996 CSE
Net Savings (BI + PIP)
Savings from IME Req but not Completed
Savings from Positive IMEs
Cost of Negative IMEs
3.8%
4.4%
0.1%
-0.7%
5.7%
2.8%
3.2%
-0.3%
8.9%
4.5%
4.9%
-0.5%
IME Performance Data% of Claims with IME Requested
Strain/ Sprain
Other Injury
1993 AIB
1996 DCD
1996 CSE 1996 CSE 1996 CSE
PIP IME (PIP Claims)
PIP IME (BI Claims)
PIP or BI IME (BI Claims)
18%
34%
41%
23%
35%
40%
20%
52%
57%
32%
53%
58%
14%
45%
51%
% of Completed IMEs with Positive Outcomes
Strain/ Sprain
Other Injury
1993 AIB
1996 DCD
1996 CSE 1996 CSE 1996 CSE
PIP IME (PIP Claims)
PIP IME (BI Claims)
PIP or BI IME (BI Claims)
34%
32%
36%
59%
60%
60%
58%
58%
70%
59%
59%
71%
54%
56%
61%
Net Savings by Suspicion Level
Suspicion Level
Claim Payment
IME Type
Claims None (0)
Low (1-3)
Mod (4-6)
High (7-10)
All
PIP Suspicion Score (CSE Model)
PIP PIP All PIPS -3% 0% 5% -6% 0%
PIP PIP PIPs with no BIs -2% 1% 2% -29% -1%
PIP PIP PIP & BI Matching -8% -1% 7% 10% 1%
BI BI PIP & BI Matching 9% 5% 8% 9% 6%
PIP+BI PIP PIP & BI Matching 4% 2% 3% 7% 4%
PIP+BI Best PIP & BI Matching 6% 5% 8% -4% 7%
BI Suspicion Score (NHR Model)
PIP PIP PIP & BI Matching 2% -2% 1% 2% 1%
BI BI PIP & BI Matching -2% 0% 11% 7% 6%
PIP+BI PIP PIP & BI Matching -7% 4% 6% 0% 4%
PIP+BI Best PIP & BI Matching -11% 0% 14% 1% 7%
Source: 1996 CSE Claims