Modeling the Settlement Modeling the Settlement Process forProcess for

Auto Bodily Injury Liability Auto Bodily Injury Liability ClaimsClaims

Richard A. Derrig,Richard A. Derrig, President, OPAL Consulting LLCPresident, OPAL Consulting LLCVisiting Scholar, Wharton SchoolVisiting Scholar, Wharton School

University of PennsylvaniaUniversity of Pennsylvania

Greg A. RempalaGreg A. RempalaAssociate Professor, StatisticsAssociate Professor, Statistics

University of LouisvilleUniversity of Louisville

CAS Predictive Modeling SeminarBoston, MA

October 4, 2006

AGENDAAGENDA

Auto BI Liability Claims are Auto BI Liability Claims are negotiated not “paid.” negotiated not “paid.”

What are the key components What are the key components of the settlement amount?of the settlement amount?

What is the role of “pain and What is the role of “pain and suffering” payments?suffering” payments?

What role does fraud and What role does fraud and build-up play?build-up play?

What are the key components What are the key components of the settlement negotiation of the settlement negotiation process itself?process itself?

NEGOTIATIONNEGOTIATION

Liability claims are negotiated Liability claims are negotiated not “paid” by the insurernot “paid” by the insurer

First party claims have payment First party claims have payment regulations both good regulations both good (Cooperation) and bad (Time (Cooperation) and bad (Time Frames for Payment) re fraud.Frames for Payment) re fraud.

Negotiation subject only to bad Negotiation subject only to bad faith and unfair claim practice faith and unfair claim practice regulationsregulations

Two-person game: Adjusters and Two-person game: Adjusters and Claimant/Attorneys, but not Claimant/Attorneys, but not suitable for game theory model.suitable for game theory model.

Example in papers is Auto Bodily Example in papers is Auto Bodily Injury Liability – Mass DataInjury Liability – Mass Data

Table 1Table 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 2Table 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

NEGOTIATIONNEGOTIATION

Claim Payment Claim Payment ComponentsComponents

Demands and OffersDemands and Offers Time Frames for RoundsTime Frames for Rounds Anchoring and AdjustingAnchoring and Adjusting Offer/Demand RatiosOffer/Demand Ratios SettlementsSettlements Mass BI Data for 1996 AYMass BI Data for 1996 AY Statistical ModelingStatistical Modeling

General DamagesGeneral Damages

Special Damages are Special Damages are Claimant Economic LossesClaimant Economic Losses– Medical BillsMedical Bills– Wage LossWage Loss– Other EconomicOther Economic

General Damages (or Pain General Damages (or Pain and Suffering payments) and Suffering payments) are the Residual of are the Residual of Negotiated Settlement Negotiated Settlement Less SpecialsLess Specials– ““Three Times Specials” is a Three Times Specials” is a

MythMyth

Figure 8-31996 Settlement/Specials Ratio Distribution

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

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

% of

Claim

s

BI 1996 Negotiations1st and 2nd Demands

$-

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

$40,000

ALL Not in Suit In Suit

Dollar

s

0

50

100

150

200

250

300

350

Claim

Cou

nts

Mean Demand 1

Mean Demand 2

Mean BISettlement

Claim Count

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

y = 1.4088x + 0.3452

R2 = 0.5691

y = 2.6414x + 1.4777

R2 = 0.1953

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

BI Settlement Ratio

First

& Se

cond

Dem

and R

atio

First Demand

Second Demand

2nd Demand Ratio

1st Demand Ratio

BI Settlement Ratio 1:1

Negotiated Negotiated SettlementsSettlements

Specials may be Specials may be Discounted or IgnoredDiscounted or Ignored

Medicals: Real or Built-up?Medicals: Real or Built-up? Information from Information from

InvestigationInvestigation Independent Medical Independent Medical

Exams (IMEs)Exams (IMEs) Special InvestigationSpecial Investigation Suspicion of Fraud or Build-Suspicion of Fraud or Build-

upup

Settlement Ratios by Injury and SuspicionSettlement Ratios by Injury and SuspicionVariableVariable PIP Suspicion PIP Suspicion

Score Score

= Low (0-3)= Low (0-3)

PIP Suspicion PIP Suspicion Score Score

= Mod to = Mod to High (4-10)High (4-10)

PIP PIP Suspicion Suspicion

Score = AllScore = All

1996 (N-336)1996 (N-336) 1996 (N-216)1996 (N-216) 1996 (N-1996 (N-552)552)

Str/Str/SPSP

All All OtherOther

Str/SPStr/SP All All OtherOther

Str/Str/SPSP

All All OtheOtherr

SettlementSettlement SettlementSettlement SettlementSettlement

81%81% 19%19% 94%94% 6%6% 86%86% 14%14%

Avg. Avg. Settlement/Settlement/Specials Specials RatioRatio

3.013.01 3.813.81 2.582.58 3.613.61 2.822.82 3.773.77

Median Median Settlement/Settlement/Specials Specials RatioRatio

2.692.69 2.892.89 2.402.40 2.572.57 2.552.55 2.892.89

Settlement ModelingSettlement Modeling

Major Claim Major Claim CharacteristicsCharacteristics

Tobit Regression for Tobit Regression for Censored Data (right Censored Data (right censored for policy limits)censored for policy limits)

Evaluation Model for Evaluation Model for Objective “Facts”Objective “Facts”

Negotiation Model for all Negotiation Model for all Other “Facts”, including Other “Facts”, including suspicion of fraud or suspicion of fraud or build-up build-up

Evaluation VariablesEvaluation Variables

Tobit Model (1996AYTobit Model (1996AY)) Claimed Medicals (+)Claimed Medicals (+) Claimed Wages (+)Claimed Wages (+) Fault (+)Fault (+) Attorney (+18%)Attorney (+18%) Fracture (+82%)Fracture (+82%) Serious Visible Injury Scene Serious Visible Injury Scene

(+36%)(+36%) Disability Weeks (+10% @ 3 Disability Weeks (+10% @ 3

weeks)weeks) Non-Emergency CT/MRI (+31%)Non-Emergency CT/MRI (+31%) Low Impact Collision (-14%)Low Impact Collision (-14%) Three Claimants in Vehicle (-Three Claimants in Vehicle (-

12%)12%) Same BI + PIP Co. (-10%) Same BI + PIP Co. (-10%)

[Passengers -22%] [Passengers -22%]

Negotiation VariablesNegotiation Variables Model Additions (1996AY)Model Additions (1996AY)

Atty (1st) Demand Ratio to Specials Atty (1st) Demand Ratio to Specials (+8% @ 6 X Specials)(+8% @ 6 X Specials)

BI IME No Show (-30%) BI IME No Show (-30%) BI IME Positive Outcome (-15%)BI IME Positive Outcome (-15%) BI IME Not Requested (-14%)BI IME Not Requested (-14%) BI Ten Point Suspicion Score (-12% @ BI Ten Point Suspicion Score (-12% @

5.0 Average)5.0 Average) [1993 Build-up Variable (-10%)][1993 Build-up Variable (-10%)] Unknown Disability (+53%)Unknown Disability (+53%) [93A (Bad Faith) Letter Not Significant][93A (Bad Faith) Letter Not Significant] [In Suit Not Significant][In Suit Not Significant] [SIU Referral (-6%) but Not Significant][SIU Referral (-6%) but Not Significant] [EUO Not Significant][EUO Not Significant]

Note: PIP IME No Show also significantly Note: PIP IME No Show also significantly reduces BI + PIP by discouraging BI reduces BI + PIP by discouraging BI claim altogether (-3%).claim altogether (-3%).

Total Value of Negotiation Total Value of Negotiation VariablesVariables

Total Compensation Total Compensation VariablesVariables

Avg. Avg. Claim/FactorClaim/Factor

Evaluation VariablesEvaluation Variables $13,948$13,948

Disability UnknownDisability Unknown 1.051.05

11stst Demand Ratio Demand Ratio 1.091.09

BI IME No ShowBI IME No Show 0.990.99

BI IME Not RequestedBI IME Not Requested 0.900.90

BI IME Performed with BI IME Performed with Positive OutcomePositive Outcome

0.970.97

SuspicionSuspicion 0.870.87

Negotiation VariablesNegotiation Variables 0.870.87

Total Compensation Model Total Compensation Model PaymentPayment

$12,058$12,058

Actual Total CompensationActual Total Compensation $11,863$11,863

Actual BI PaymentActual BI Payment $8,551$8,551

Actual parameters Actual parameters for negotiation and for negotiation and evaluation models, evaluation models, with and without with and without

suspicion variable, suspicion variable, are shown in the are shown in the

hard copy handouthard copy handout

NEGOTIATIONNEGOTIATION

Claim Payment Claim Payment ComponentsComponents

Demands and OffersDemands and Offers Time Frames for RoundsTime Frames for Rounds Anchoring and AdjustingAnchoring and Adjusting Offer/Demand RatiosOffer/Demand Ratios SettlementsSettlements Mass BI Data for 1996 AYMass BI Data for 1996 AY Statistical ModelingStatistical Modeling

STAT. MODELINGSTAT. MODELING

Identify Identify random componentrandom component of of negotiation process (in any)negotiation process (in any)

Demands and offers not Demands and offers not independent independent

Claims sizes form mixtures of Claims sizes form mixtures of dists dists

Assume: current O (D) depend Assume: current O (D) depend only on the previous O, Donly on the previous O, D

Markov Chain ?Markov Chain ? Time frames for rounds seem Time frames for rounds seem

homonegous (possibly homonegous (possibly deterministic) deterministic)

Consider O/D values in a single Consider O/D values in a single claim negotiation claim negotiation

A Statistical Analysis of the A Statistical Analysis of the Effect of Anchoring in the Effect of Anchoring in the

Negotiation Process of Negotiation Process of Automobile Bodily Injury Automobile Bodily Injury

Liability ClaimsLiability Claims

Richard A. Derrig,Richard A. Derrig, President, OPAL Consulting LLCPresident, OPAL Consulting LLCVisiting Scholar, Wharton SchoolVisiting Scholar, Wharton School

University of PennsylvaniaUniversity of Pennsylvania

Greg A. RempalaGreg A. RempalaAssociate Professor, StatisticsAssociate Professor, Statistics

University of LouisvilleUniversity of Louisville

Working Paper v 3.1Working Paper v 3.1March 10, 2006March 10, 2006

Table 6Table 6

Negotiation – Offer/Demand Ratios by Round

4 ROUNDS (100 claims)

O1/D1 O2/D2 O3/D3 BI/D3

Average 0.246 0.476 0.724 0.798

Std. Dev. 0.153 0.213 0.211 0.191

3 ROUNDS (119 claims)

O1/D1 O2/D2 BI/D2

Average 0.393 0.708 0.766

Std. Dev. 0.610 0.212 0.191

O/D ProcessO/D Process

0 1

Initial Settlement

O1/D1 O2/D2 O3/D3

OOii/D/Dii values are non values are non decreasing, should tend to decreasing, should tend to one (settlement)one (settlement) Considering O/D Considering O/D homogenizes the data from homogenizes the data from different claim negotiations, different claim negotiations, but:but: Disregards Disregards timetime and and claim claim sizesize Possibly removes some Possibly removes some other covariates (Injury, etc)other covariates (Injury, etc)

Offer Demand Ratios (Sorted Offer Demand Ratios (Sorted by Descending Losses) – by Descending Losses) –

FigureFigure 11

Offer Demand Ratios (Sorted by Offer Demand Ratios (Sorted by Descending 1st Demands) – Figure Descending 1st Demands) – Figure

22

O/D as Poisson ProcessO/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 EstimationRate Estimation

(t) may be approximated by a piecewise function

Decide on a time interval within Decide on a time interval within which rate is fixedwhich rate is fixed

Estimate from O/D data the Estimate from O/D data the (constant) rate during each (constant) rate during each intervalinterval

Easy simulation of NHPP with Easy simulation of NHPP with piecewise constant piecewise constant (t) using rejection method

t

( ) t

Rates ComparisonRates 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: Figure 1: The Massachusetts Negotiation Data The Massachusetts Negotiation Data

Estimated standardized rates of the NHPP of Estimated standardized rates of the NHPP of arrival of O/D for 2-, 3- and 4-negotiation arrival of O/D for 2-, 3- and 4-negotiation

rounds.rounds.

Rates comparison (cont)Rates comparison (cont)

Seems that the Mass. data Seems that the Mass. data induces two types of rates:induces two types of rates:

Slow rate (2 rounds)Slow rate (2 rounds) Fast rate (3 or more rounds) Fast rate (3 or more rounds) Can we predict the rate type Can we predict the rate type

from the initial set of covariates from the initial set of covariates ??

Use logistic regression for Use logistic regression for classificationclassification

Simple, yet satisfying (error: Simple, yet satisfying (error: 18% on data, 20% on cross-18% on data, 20% on cross-valildation)valildation)

Comparable to SVM and othersComparable to SVM and others

Table 10Table 10

Logistic Classifier of Fast and Slow Claims

Variable CoefficientStandard

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:Figure 3:95% confidence tunnel for both ‘slow’ and 95% confidence tunnel for both ‘slow’ and

‘fast’ fitted rates for the subset of 58 ‘fast’ fitted rates for the subset of 58 negotiations histories from the negotiations histories from the

Massachusetts datasetMassachusetts dataset

Table 7Table 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 Offer / Demand Ratios (Sorted by Descending Pre-(Sorted by Descending Pre-Settlement Ratio) – Figure 3Settlement Ratio) – Figure 3

Simulated vs True O/D DataSimulated vs True O/D Data

Alternative approach:Alternative approach:SVM classifier SVM classifier

Drive a hyperplane across data to Drive a hyperplane across data to separate FAST/SLOW claims 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:Alternative approach:SVM classifier (cont)SVM classifier (cont)

If data separable, pick a hyperplane with If data separable, pick a hyperplane with largest possible margin largest possible margin Otherwise penalty for misclassification Often Often data may be separable after space transformation

NEGOTIATIONNEGOTIATIONFuture Modeling Future Modeling

Work Work Demands and OffersDemands and Offers Role of Time Frames Role of Time Frames Role of Covariates (Injury, Role of Covariates (Injury,

etc)etc) Anchoring and AdjustingAnchoring and Adjusting Offer/Demand RatiosOffer/Demand Ratios SettlementsSettlements Statistical ModelsStatistical Models Mass BI Data for 1996 AYMass BI Data for 1996 AY Another Data Set NeededAnother Data Set Needed

ReferencesReferences Cooter, Robert D. and Daniel L. Rubinfeld, (1989), Cooter, Robert D. and Daniel L. Rubinfeld, (1989),

Economic Analysis of Legal Disputes and Their Economic Analysis of Legal Disputes and Their Resolution, Resolution, Journal of Economic LiteratureJournal of Economic Literature, 27, 1067-, 27, 1067-10971097

Derrig, Richard, and Herbert I. Weisberg, (2004), Derrig, Richard, and Herbert I. Weisberg, (2004), Determinants of Total Compensation for Auto Bodily Determinants of Total Compensation for Auto Bodily Injury Liability Under No Fault: Investigation, Injury Liability Under No Fault: Investigation, Negotiation and the Suspicion of Fraud, Negotiation and the Suspicion of Fraud, Insurance and Insurance and Risk ManagementRisk Management, 71:4, 633-662, January., 71:4, 633-662, January.

Epley, Nicholas, and Thomas Gilovich, (2001), Putting Epley, Nicholas, and Thomas Gilovich, (2001), Putting Adjustment Back in the Anchoring and Adjustment Adjustment Back in the Anchoring and Adjustment Heuristic: Differential Processing of Self-Generated and Heuristic: Differential Processing of Self-Generated and Experimenter-Provided Anchors, Experimenter-Provided Anchors, Psychological SciencePsychological Science, , 12:5, 391-396.12:5, 391-396.

Loughran, David, (2005) Deterring Fraud: The Role of Loughran, David, (2005) Deterring Fraud: The Role of General Damage Awards in Automobile Insurance General Damage Awards in Automobile Insurance Settlements, Settlements, Journal of Risk and Insurance, Journal of Risk and Insurance, 72:551-57572:551-575

Raiffa, Howard, (1982), Raiffa, Howard, (1982), The Art and Science of The Art and Science of Negotiation, Negotiation, The Belknap Press of Harvard University The Belknap Press of Harvard University Press.Press.

Ross, Lawrence, H., (1980), Ross, Lawrence, H., (1980), Settled Out of CourtSettled Out of Court, , (Chicago, III: Aldine).(Chicago, III: Aldine).

Tversky, A., and D. Kahneman, (1974), Judgment Under Tversky, A., and D. Kahneman, (1974), Judgment Under Uncertainty: Heuristics and Biases, Uncertainty: Heuristics and Biases, ScienceScience, 195, 1124-, 195, 1124-1130.1130.

Wright, W.F. and U. Anderson, (1989), Effects of Wright, W.F. and U. Anderson, (1989), Effects of Situation Familiarity and Incentives on use of the Situation Familiarity and Incentives on use of the Anchoring and Adjustment Heuristic for Probability Anchoring and Adjustment Heuristic for Probability Assessment, Assessment, Organizational Behavior and Human Organizational Behavior and Human Decision ProcessesDecision Processes, 44, 68-82., 44, 68-82.