Modeling the Settlement
Process for
Auto Bodily Injury Liability
Claims
Richard A. Derrig,
President, OPAL Consulting LLC
Visiting Scholar, Wharton School
University of Pennsylvania
Greg A. Rempala
Associate Professor, Statistics
University of Louisville
CAS Predictive Modeling Seminar
Boston, MA
October 4, 2006
AGENDA
Auto BI Liability Claims are
negotiated not “paid.”
 What are the key components
of the settlement amount?
 What is the role of “pain and
suffering” payments?
 What role does fraud and
build-up play?
 What are the key components
of the settlement negotiation
process itself?

NEGOTIATION





Liability claims are negotiated not
“paid” by the insurer
First party claims have payment
regulations both good
(Cooperation) and bad (Time
Frames for Payment) re fraud.
Negotiation subject only to bad
faith and unfair claim practice
regulations
Two-person game: Adjusters and
Claimant/Attorneys, but not
suitable for game theory model.
Example in papers is Auto Bodily
Injury Liability – Mass Data
Table 1
BI Negotiation Leverage Points
Adjuster Advantages
Adjuster has ability to go to trial
Company has the settlement funds
Attorney, provider, or claimant needs money
Adjuster knows history of prior settlements
Adjuster can delay settlement by investigation
Settlement authorization process in company
Initial Determination of Liability
Table 2
BI Negotiation Leverage Points
Attorney/Claimant Advantages
Attorney/Claimant can build-up specials
Asymmetric information
(Accident, Injury, Treatment)
Attorney/Claimant can fail to cooperate
Attorney has experience with company
Investigation costs the company money
Attorney can allege unfair claim
practices (93A)
Adjuster under pressure to close files
NEGOTIATION
 Claim
Payment
Components
 Demands and Offers
 Time Frames for Rounds
 Anchoring and Adjusting
 Offer/Demand Ratios
 Settlements
 Mass BI Data for 1996 AY
 Statistical Modeling
General Damages

Special Damages are Claimant
Economic Losses
– Medical Bills
– Wage Loss
– Other Economic

General Damages (or Pain and
Suffering payments) are the
Residual of Negotiated
Settlement Less Specials
– “Three Times Specials” is a Myth
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 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
Settlement/Specials Ratio
BI 1996 Negotiations
1st and 2nd Demands
$40,000
350
$35,000
300
$30,000
Dollars
$25,000
200
$20,000
150
$15,000
Claim Counts
250
Mean Demand 1
Mean Demand 2
Mean BI
Settlement
Claim Count
100
$10,000
50
$5,000
$-
0
ALL
Not in Suit
In Suit
CSE: First & Second Demand Ratio to BI Settlement Ratio
Limited to 2nd Demand > $0, (315 BI Claims)
NO PIP payment in Demand & Settlement, Outlier removed 3860
20
y = 2.6414x + 1.4777
R2 = 0.1953
18
1st Demand Ratio
First & Second Demand Ratio
16
y = 1.4088x + 0.3452
R2 = 0.5691
2nd Demand Ratio
14
BI Settlement Ratio 1:1
12
10
8
First Demand
Second Demand
6
4
2
0
0
2
4
6
8
10
BI Settlement Ratio
12
14
16
18
20
Negotiated Settlements
Specials may be Discounted or
Ignored
 Medicals: Real or Built-up?
 Information from Investigation
 Independent Medical Exams
(IMEs)
 Special Investigation
 Suspicion of Fraud or Build-up

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/S
P
All
Other
Settlement
81%
19%
94%
6%
86%
14%
Avg.
Settlement/Sp
ecials Ratio
3.01
3.81
2.58
3.61
2.82
3.77
Median
Settlement/Sp
ecials Ratio
2.69
2.89
2.40
2.57
2.55
2.89
Settlement Modeling




Major Claim Characteristics
Tobit Regression for Censored
Data (right censored for
policy limits)
Evaluation Model for
Objective “Facts”
Negotiation Model for all
Other “Facts”, including
suspicion of fraud or buildup
Evaluation Variables











Tobit Model (1996AY)
Claimed Medicals (+)
Claimed Wages (+)
Fault (+)
Attorney (+18%)
Fracture (+82%)
Serious Visible Injury Scene (+36%)
Disability Weeks (+10% @ 3 weeks)
Non-Emergency CT/MRI (+31%)
Low Impact Collision (-14%)
Three Claimants in Vehicle (-12%)
Same BI + PIP Co. (-10%)
[Passengers -22%]
Negotiation Variables
Model Additions (1996AY)
Atty (1st) Demand Ratio to Specials (+8%
@ 6 X Specials)
 BI IME No Show (-30%)
 BI IME Positive Outcome (-15%)
 BI IME Not Requested (-14%)
 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
Actual parameters for
negotiation and
evaluation models,
with and without
suspicion variable, are
shown in the hard
copy handout
NEGOTIATION
 Claim
Payment
Components
 Demands and Offers
 Time Frames for Rounds
 Anchoring and Adjusting
 Offer/Demand Ratios
 Settlements
 Mass BI Data for 1996 AY
 Statistical Modeling
STAT. MODELING







Identify random component of
negotiation process (in any)
Demands and offers not
independent
Claims sizes form mixtures of dists
Assume: current O (D) depend only
on the previous O, D
Markov Chain ?
Time frames for rounds seem
homonegous (possibly
deterministic)
Consider O/D values in a single
claim negotiation
A Statistical Analysis of the Effect of
Anchoring in the Negotiation
Process of Automobile Bodily Injury
Liability Claims
Richard A. Derrig,
President, OPAL Consulting LLC
Visiting Scholar, Wharton School
University of Pennsylvania
Greg A. Rempala
Associate Professor, Statistics
University of Louisville
Working Paper v 3.1
March 10, 2006
Table 6
Negotiation –
Offer/Demand Ratios by Round
4 ROUNDS (100 claims)
O1/D1 O2/D2
O3/D3
Average
Std. Dev.
0.246 0.476
0.724
0.153 0.213
0.211
3 ROUNDS (119 claims)
Average
O1/D1
0.393
O2/D2
0.708
BI/D2
0.766
Std. Dev.
0.610
0.212
0.191
BI/D3
0.798
0.191
O/D Process
Initial
0
O1/D1
Oi/Di
Settlement
1
O2/D2
O3/D3
values are non decreasing,
should tend to one (settlement)
 Considering O/D homogenizes
the data from different claim
negotiations, but:
Disregards time and claim size
Possibly removes some other
covariates (Injury, etc)
Offer Demand Ratios (Sorted by
Descending Losses) – Figure 1
Offer Demand Ratios (Sorted by
Descending 1st Demands) – Figure 2
O/D as Poisson Process
Nt number of discrete events
on (0,t] arriving “one at a time”
 Nt is NHPP with rate (t), if for
every t>0
P(Nt =k)=exp(-z(t)) [z(t)] k/k!.
where z(t)=0t (s)ds
 NHPP is uniquely determined
by its rate function (t)
 Distance between Oi/Di and
Oi+1/Di+1 is exponential with
rate (t)
 How to estimate (t) ?

Rate Estimation

(t) may be approximated by a
piecewise function
 Decide on a time interval within
which rate is fixed
 Estimate from O/D data the
(constant) rate during each interval
 (t )
t
Easy simulation of NHPP with
piecewise constant (t) using
rejection method
Rates Comparison

(t) is the average “speed” of
negotiation measured in O/D
ratio increase rate
 Is it the same for all claims ?
 Simple statistical test based on
parametric resampling
 95 % confidence envelopes
(tunnels)
 No evidence of difference in
(t) for 3 and 4 rounds (lay within
each other tunnels)
 (t) for 2 round is significantly
different
Figure 1:
The Massachusetts Negotiation Data
Estimated standardized rates of the NHPP of arrival
of O/D for 2-, 3- and 4-negotiation rounds.
Rates comparison (cont)
Seems that the Mass. data
induces two types of rates:
 Slow rate (2 rounds)
 Fast rate (3 or more rounds)
 Can we predict the rate type
from the initial set of
covariates ?
 Use logistic regression for
classification
 Simple, yet satisfying (error:
18% on data, 20% on crossvalildation)
 Comparable to SVM and others

Table 10
Logistic Classifier of Fast and Slow Claims
Variable
Standard
Coefficient
Error
p-Value
Demand 1 (000's)
-0.0678
0.0327
0.0385
O1 / D1
-5.4660
2.8440
0.0546
Report Date –
Accident Date
(days)
-0.0297
0.0103
0.0038
Three or more
claimants
-1.6990
1.0580
0.1082
BI IME Not
Requested
3.1300
1.0940
0.0042
BI IME Performed
with Positive
Outcome
2.5460
1.4490
0.0789
Intercept
3.0120
1.7000
0.0764
Figure 3:
95% confidence tunnel for both ‘slow’ and ‘fast’
fitted rates for the subset of 58 negotiations
histories from the Massachusetts dataset
Table 7
Offer/Demand Ratio Dependence on Demand
Ratio
Rounds
Intercept
Int.
S.E.
Demand
(000)
Coefficient
O1/D1
2
0.55
0.08
-0.0074
O2/D2
2
0.78
0.02
-0.0061
BI/D2
2
0.84
0.02
-0.0057
O1/D1
3
0.28
0.02
-0.0013
O2/D2
3
0.56
0.03
-0.0055
O3/D3
3
0.79
0.03
-0.0058
BI/D3
3
0.84
0.02
-0.0040
All intercept and demand coefficients significant at
1%
Offer / Demand Ratios
(Sorted by Descending PreSettlement Ratio) – Figure 3
Simulated vs True O/D Data
Alternative approach:
SVM classifier
Drive a hyperplane across data to separate
FAST/SLOW claims
 Prediction: On which side of the hyperplane does
the new point lie?
 Points in the direction of the normal vector are
classified as POSITIVE (fast); otherwise
NEGATIVE (slow).

Alternative approach:
SVM classifier (cont)
If data separable, pick a hyperplane with
largest possible margin
 Otherwise penalty for misclassification
 Often data may be separable after space
transformation

NEGOTIATION
Future Modeling Work
Demands and Offers
Role of Time Frames
 Role of Covariates (Injury, etc)

 Anchoring
and Adjusting
 Offer/Demand Ratios
 Settlements
 Statistical Models
 Mass BI Data for 1996 AY
 Another Data Set Needed
References
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Cooter, Robert D. and Daniel L. Rubinfeld, (1989),
Economic Analysis of Legal Disputes and Their
Resolution, Journal of Economic Literature, 27, 10671097
Derrig, Richard, and Herbert 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, 71:4, 633-662, January.
Epley, Nicholas, and Thomas Gilovich, (2001), Putting
Adjustment Back in the Anchoring and Adjustment
Heuristic: Differential Processing of Self-Generated
and Experimenter-Provided Anchors, Psychological
Science, 12:5, 391-396.
Loughran, David, (2005) Deterring Fraud: The Role of
General Damage Awards in Automobile Insurance
Settlements, Journal of Risk and Insurance, 72:551575
Raiffa, Howard, (1982), The Art and Science of
Negotiation, The Belknap Press of Harvard University
Press.
Ross, Lawrence, H., (1980), Settled Out of Court,
(Chicago, III: Aldine).
Tversky, A., and D. Kahneman, (1974), Judgment
Under Uncertainty: Heuristics and Biases, Science,
195, 1124-1130.
Wright, W.F. and U. Anderson, (1989), Effects of
Situation Familiarity and Incentives on use of the
Anchoring and Adjustment Heuristic for Probability
Assessment, Organizational Behavior and Human
Decision Processes, 44, 68-82.