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Closure-Based Regression Method Stephen Marsden , FCAS, MAAA

Closure-Based Regression Method Stephen Marsden , FCAS, MAAA. Closure-Based Regression Method. Should Paid Loss Be Developed Based on Age or Closure ?. Closure-Based Regression Method. Test by use of simple regression

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Closure-Based Regression Method Stephen Marsden , FCAS, MAAA

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  1. Closure-Based Regression MethodStephen Marsden, FCAS, MAAA

  2. Closure-Based Regression Method Should Paid Loss Be Developed Based on Age or Closure ?

  3. Closure-Based Regression Method Test by use of simple regression • First regression: Age as a predictor of Paid LDF from age of data point to age 51 • Second regression: Closure as a predictor of Paid LDF from closure of data point to 99.9% closed Age = Accident Year Age in Months Closure = Closed Claims with Payment / (Closed Claims with Payment + Open Claims)

  4. Closure-Based Regression Method Age-Based Regression

  5. Closure-Based Regression Method Closure-Based Regression

  6. Closure-Based Regression Method Same data grouped by age (top slide) and closure (bottom slide) from a large book of personal lines non-standard auto business (high frequency and low severity)

  7. Closure-Based Regression Method • Amazingly tight fit for Bodily Injury using only simple regression !!! • Visual evidence is compelling and provides confidence • Age is definitely less predictive than closure • Multiple regression may only add incremental benefit w/ added complexity for paid approach • The variance shown at young ages is not trend but represents only differences in closure • A very accurate loss development pattern can be established at a 35% closure ratio

  8. Closure-Based Regression Method Similar To The Berquist Sherman Method • Replaces an age-based concept with a closure-based concept • Adds most value when settlement rates change in time • Leverages the fact that age is a poor surrogate for closure rate • Traditional methods may incorrectly develop losses • Sudden increase in settlement rate likely will lead to over-projection • Sudden decrease in settlement rate likely will lead to under-projection

  9. Closure-Based Regression Method Berquist Sherman Method • Traditional triangle-based chain ladder approach • Counts and interpolation to replace an age-based triangle with a closure-based triangle Closure-Based Regression Method • Uses a direct simple regression of the relationship between closure ratio and LDF • Provides visual evidence of the relationship to LDF

  10. Closure-Based Regression Method Advantages Over Berquist Sherman • Provides visual evidence of the relationship of age or closure to LDF • Directly Measures Relationship and Does Not Add Error Thru • Chain Ladder Approach • Interpolation In Reconstructing Triangle Disadvantage To Berquist Sherman • Berquist Sherman Utilizes More Recent Data

  11. Closure-Based Regression Method Case Reserves Do Not Help Fit • Case Reserves may be More Related to Age • .99 r^2 hard to improve upon especially considering principal of parsimony • Multiple Regression or Separate Method to Leverage Case Reserves Beware of Changes in Count Data and Changes in The Fitted LDF Curve Age-Based Paid Development Methods – When to Give No Weight Age-Based Incurred Development Methods – A Mixed Bag

  12. Closure-Based Regression Method Questions Before Mechanics of Method?

  13. Closure-Based Regression Method Mechanics: Brief Overview • Retrospective Review of 2 Data Elements • Closure Ratio CWA / (CWA + Open) • Paid LDF Paid at that Closure Ratio to Paid at 99% Closed (Tail Later) • Collect These Data Elements at Multiple Data Points and Regress • Triangle is Not Required

  14. Closure-Based Regression Method Exhibit 1 CWA / (CWA + Open)

  15. Closure-Based Regression Method Exhibit 2 Net Paid Loss & ALAE

  16. Closure-Based Regression Method Exhibit 3

  17. Closure-Based Regression Method Exhibit 4 Net Paid Loss & ALAE Closure Point to 99% Closed LDF 792.311= 18,896,622 / 23,850

  18. Closure-Based Regression Method Exhibit 5 LDF from Point to 99% Closed % Closed at Point

  19. Closure-Based Regression Method • After Data Organized Perform Regressions as in slide 6 • Test Relative Strength of Fits of Age Regression vs. Closure Regression • One Curve or Splines ?

  20. Closure-Based Regression Method In this case we have fit two curves to the data • The first curve fits to 80% closed • The second curve fits from 80% closed to 99% closed

  21. Closure-Based Regression Method

  22. Closure-Based Regression Method

  23. Exhibit 9 Closure-Based Regression Method % Closed to 80% Closed Regression 80% Closed to 99% Closed Regression

  24. Closure-Based Regression Method Exhibit 10

  25. Exhibit 11 Closure-Based Regression Method

  26. Exhibit 11 Worksheet Closure-Based Regression Method .7271x(.5669)^(-1.3997)=1.609 .9825x(.8945)^(-1.5244)=1.165 .9825x(.8000)^(-1.5244)=1.381

  27. Closure-Based Regression Method Questions ?

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