Modeling the Settlement Process for Auto Bodily Injury Liability Claims Richard A. Derrig, President, OPAL Consulting LLC Visiting Scholar, Wharton School President, OPAL Consulting LLC Visiting Scholar, Wharton School University of Pennsylvania 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.” Auto BI Liability Claims are negotiated not “paid.” What are the key components of the settlement amount? What are the key components of the settlement amount? What is the role of “pain and suffering” payments? What is the role of “pain and suffering” payments? What role does fraud and build-up play? What role does fraud and build-up play? What are the key components of the settlement negotiation process itself? What are the key components of the settlement negotiation process itself?

NEGOTIATION Liability claims are negotiated not “paid” by the insurer 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. 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 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. Two-person game: Adjusters and Claimant/Attorneys, but not suitable for game theory model. Example in papers is Auto Bodily Injury Liability – Mass Data 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 Claim Payment Components Demands and Offers Demands and Offers Time Frames for Rounds Time Frames for Rounds Anchoring and Adjusting Anchoring and Adjusting Offer/Demand Ratios Offer/Demand Ratios Settlements Settlements Mass BI Data for 1996 AY Mass BI Data for 1996 AY Statistical Modeling Statistical Modeling

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

Negotiated Settlements Specials may be Discounted or Ignored Specials may be Discounted or Ignored Medicals: Real or Built-up? Medicals: Real or Built-up? Information from Investigation Information from Investigation Independent Medical Exams (IMEs) Independent Medical Exams (IMEs) Special Investigation Special Investigation Suspicion of Fraud or Build-up Suspicion of Fraud or Build-up

Independent Medical Exams Policy Requirement (Mass) Policy Requirement (Mass) General Claim Information plus Medical Examination General Claim Information plus Medical Examination Outcomes Outcomes –No change recommended –Refused or no show –Damages mitigated or –Treatment curtailed Cost ($350, $75 no show) Cost ($350, $75 no show)

IME Savings PIP & BI PIP Sample: 1996 CSE Net Savings (PIP) -0.8% Savings from IME Requ but not Comp Savings from IME Requ but not Comp0.7% Savings from Positive IMEs Savings from Positive IMEs-0.4% Cost of Negative IMEs Cost of Negative IMEs-1.1% PIP+BI Sample: 1996 CSE Net Savings (PIP+BI) 8.7% Savings from IME Requ but not Comp* Savings from IME Requ but not Comp*4.3% Savings from Positive IMEs Savings from Positive IMEs4.9% Cost of Negative IMEs 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.

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 Str/SP Str/S P All Other SettlementSettlementSettlement 81%19%94%6%86%14% Avg. Settlement/Sp ecials Ratio Median Settlement/Sp ecials Ratio

Breakdown of Same/Different Company Claims Count Total Pay Total Med % Injuries Serious Frac All Claims 429$13,346$4,7705.8% Same Company Claims 118$13,246$4,9699.3% Same Co./Same Policy- Clmt is Pass Same Co./Same Policy- Clmt is Pass41$11,029$5, % Same Co./Same Policy- Clmt is Pedestr Same Co./Same Policy- Clmt is Pedestr22$17,862$5, % Same Co./Same Policy- Uninsured Clm Same Co./Same Policy- Uninsured Clm16 $ 9,416 $3,9310.0% Same Co./Different Policy Same Co./Different Policy39$14,542$4,9365.1% Different Company Claims Different Company Claims311$13,383$4,6954.5%

Comparison of Known Disability Claims vs. Unknown Disability Claims No. / Percent of ClaimsMean* UnknownKnownUnknownKnown Total Paid63429$16,765$13,346 Medical Settlement64429$6,387$4,546 Wage Settlement0102$0$3,578 First Demand46376$26,298$23,924 Second Demand19240$22,342$12,745 Average Weekly Wage11116$455$569 Sprain/Strain Only58%61% Primary Provider CH PT MD 14% 31% 53% 46% 22% 31% BI Suspicion Score PIP Suspicion Score * mean calculation of non-zero entries

Settlement Modeling Major Claim Characteristics Major Claim Characteristics Tobit Regression for Censored Data (right censored for policy limits) Tobit Regression for Censored Data (right censored for policy limits) Evaluation Model for Objective “Facts” Evaluation Model for Objective “Facts” Negotiation Model for all Other “Facts”, including suspicion of fraud or build- up Negotiation Model for all Other “Facts”, including suspicion of fraud or build- up

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

Negotiation Variables Model Additions (1996AY) Model Additions (1996AY) Atty (1st) Demand Ratio to Specials 6 X Specials) Atty (1st) Demand Ratio to Specials 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 5.0 Average) BI Ten Point Suspicion Score 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 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 st Demand Ratio 1.09 BI IME No Show 0.99 BI IME Not Requested 0.90 BI IME Performed with Positive Outcome 0.97 Suspicion0.87 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 Claim Payment Components Demands and Offers Demands and Offers Time Frames for Rounds Time Frames for Rounds Anchoring and Adjusting Anchoring and Adjusting Offer/Demand Ratios Offer/Demand Ratios Settlements Settlements Mass BI Data for 1996 AY Mass BI Data for 1996 AY Statistical Modeling Statistical Modeling

STAT. MODELING Identify random component of negotiation process (in any) Identify random component of negotiation process (in any) Demands and offers not independent Demands and offers not independent Claims sizes form mixtures of dists Claims sizes form mixtures of dists Assume: current O (D) depend only on the previous O, D Assume: current O (D) depend only on the previous O, D Markov Chain ? Markov Chain ? Time frames for rounds seem homonegous (possibly deterministic) Time frames for rounds seem homonegous (possibly deterministic) Consider O/D values in a single claim negotiation 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 President, OPAL Consulting LLC Visiting Scholar, Wharton School University of Pennsylvania 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) O 1 /D 1 O 2 /D 2 O 3 /D 3 BI/D 3 Average Std. Dev ROUNDS (119 claims) O 1 /D 1 O 2 /D 2 BI/D 2 Average Std. Dev

O/D Process 0 1 Initial Settlement O 1 /D 1 O 2 /D 2 O 3 /D 3 O i /D i values are non decreasing, should tend to one (settlement) O i /D i values are non decreasing, should tend to one (settlement) Considering O/D homogenizes the data from different claim negotiations, but: Considering O/D homogenizes the data from different claim negotiations, but: Disregards time and claim size Disregards time and claim size Possibly removes some other covariates (Injury, etc) 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 N t number of discrete events on (0,t] arriving “one at a time” N t is NHPP with rate (t), if for every t>0 P(N t =k)=exp(-z(t)) [z(t)] k /k!. where z(t)=  0 t (s)ds NHPP is uniquely determined by its rate function (t) Distance between O i /D i and O i+1 /D i+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 Easy simulation of NHPP with piecewise constant Easy simulation of NHPP with piecewise constant (t) using rejection method t

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: Seems that the Mass. data 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 from the initial set of covariates ? Can we predict the rate type from the initial set of covariates ? Use logistic regression for classification Use logistic regression for classification Simple, yet satisfying (error: 18% on data, 20% on cross- valildation) Simple, yet satisfying (error: 18% on data, 20% on cross- valildation) Comparable to SVM and others Comparable to SVM and others

Table 10 Logistic Classifier of Fast and Slow Claims VariableCoefficient Standard Errorp-Value Demand 1 (000's) O 1 / D Report Date – Accident Date (days) Three or more claimants BI IME Not Requested BI IME Performed with Positive Outcome Intercept

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 RatioRoundsInterceptInt. S.E. Demand (000) Coefficient O 1 /D O 2 /D BI/D O 1 /D O 2 /D O 3 /D BI/D All intercept and demand coefficients significant at 1%

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

Simulated vs True O/D Data

Alternative approach: SVM classifier Drive a hyperplane across data to separate FAST/SLOW claims 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 If data separable, pick a hyperplane with largest possible margin Otherwise penalty for misclassification Often Often data may be separable after space transformation

NEGOTIATION Future Modeling Work Demands and Offers Demands and Offers Role of Time Frames Role of Time Frames Role of Covariates (Injury, etc) Role of Covariates (Injury, etc) Anchoring and Adjusting Anchoring and Adjusting Offer/Demand Ratios Offer/Demand Ratios Settlements Settlements Statistical Models Statistical Models Mass BI Data for 1996 AY Mass BI Data for 1996 AY Another Data Set Needed Another Data Set Needed

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