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Modeling the Settlement Process for Auto Bodily Injury Liability Claims

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 .

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Modeling the Settlement Process for Auto Bodily Injury Liability Claims

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  1. Modeling the Settlement Process for Auto Bodily Injury Liability Claims Richard A. Derrig, President, OPAL Consulting LLCVisiting Scholar, Wharton School University of Pennsylvania Greg A. Rempala Associate Professor, Statistics University of Louisville CAS Predictive Modeling Seminar Boston, MA October 4, 2006

  2. 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?

  3. 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

  4. Table 1

  5. Table 2

  6. 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

  7. 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

  8. 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

  9. 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 build-up

  10. 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%]

  11. 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%).

  12. Total Value of Negotiation Variables

  13. Actual parameters for negotiation and evaluation models, with and without suspicion variable, are shown in the hard copy handout

  14. 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

  15. 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

  16. A Statistical Analysis of the Effect of Anchoring in the Negotiation Process of Automobile Bodily Injury Liability Claims Richard A. Derrig, President, OPAL Consulting LLCVisiting Scholar, Wharton School University of Pennsylvania Greg A. Rempala Associate Professor, Statistics University of Louisville Working Paper v 3.1 March 10, 2006

  17. Table 6

  18. O/D Process Initial Settlement 1 0 O1/D1 O3/D3 O2/D2 • Oi/Di 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)

  19. Offer Demand Ratios (Sorted by Descending Losses) – Figure1

  20. Offer Demand Ratios (Sorted by Descending 1st Demands) – Figure 2

  21. 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 isexponential with rate (t) • How to estimate (t) ?

  22. 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 (t) using rejection method

  23. Rates Comparison • (t) is the average “speed” of negotiation measuredin O/Dratio 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

  24. Figure 1: The Massachusetts Negotiation Data Estimated standardized rates of the NHPP of arrival of O/D for 2-, 3- and 4-negotiation rounds.

  25. 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 cross-valildation) • Comparable to SVM and others

  26. Table 10

  27. Figure 3:95% confidence tunnel for both ‘slow’ and ‘fast’ fitted rates for the subset of 58 negotiations histories from the Massachusetts dataset

  28. Table 7

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

  30. Simulated vs True O/D Data

  31. 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).

  32. 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

  33. NEGOTIATIONFuture 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

  34. References • Cooter, Robert D. and Daniel L. Rubinfeld, (1989), Economic Analysis of Legal Disputes and Their Resolution, Journal of Economic Literature, 27, 1067-1097 • 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, 72:551-575 • 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.

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