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The Analysis and Estimation of Loss & ALAE Variability

The Analysis and Estimation of Loss & ALAE Variability Section 5. Compare, Contrast and Discuss Results Dr Julie A Sims Casualty Loss Reserve Seminar Boston, MA September 13, 2005. Data. Model. And the Winner is…. It depends on the aims of the analysis

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The Analysis and Estimation of Loss & ALAE Variability

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  1. The Analysis and Estimation of Loss & ALAE Variability Section 5. Compare, Contrast and Discuss Results Dr Julie A Sims Casualty Loss Reserve SeminarBoston, MASeptember 13, 2005

  2. Data Model And the Winner is… • It depends on the aims of the analysis • It depends on the data you are analysing • Finding the model that works best “on average” is a huge amount of work – more than this Working Party could do

  3. More Limited Aim • Give some examples and ideas of how to use the criteria • Get people thinking and talking about the need to do more

  4. 3 Star Modelling Process Fit for purpose: Criteria 1, 2, 3, 4 Adequate fit: Criteria 14, 15 Best in class: Criteria 5, 6, 7, 8, 10, 11, 13, 16, 17, 18, 20 Orphans 9, 12, 19

  5. Fit For Purpose: Criterion 1 Aims of the Analysis • Expected Range (ER): unreliable estimates of parameter uncertainty and percentiles • Overdispersed Poisson (ODP): no estimates of percentiles • Mack chain ladder equivalent (distribution free): no estimates of percentiles • Murphy average ratio equivalent (with normal distribution): full distribution

  6. Fit For Purpose: Criterion 4 Cost/Benefit • ER: low cost • Mack & Murphy: moderate cost • ODP: higher cost • “Cost” here is based on complexity • Benefits? – see later

  7. Adequate Fit: Criterion 14 Distributional Assumptions • Essential if you want percentiles • ER, Mack & ODP: no distribution • Murphy on IL40: poor normality = poor fit

  8. Adequate Fit: Criterion 14Distributional Assumptions Murphy on IL40

  9. Adequate Fit: Criterion 14Distributional Assumptions Murphy on IL40

  10. Adequate Fit: Criterion 15 Residual Patterns • Patterns in residuals likely to give a poor estimate of the mean • ER: residuals not defined • Murphy on IL40 and ODP on PL40: poor fit

  11. Adequate Fit: Criterion 15Residual Patterns • Murphy on IL40: residuals trend up in later accident periods, forecast means likely to be too low

  12. Adequate Fit: Criterion 15Residual Patterns • ODP on PL40: residuals trend up and down over calendar periods, forecast means might be high or low

  13. Best in Class: 11 Criteria! • No surprising behaviour • Parsimony - as few parameters as is consistent with good fit

  14. Best in Class: Criterion 5CV Decreases in Later Accident Periods • ER on PL40: surprising increases in coefficient of variation of accident totals

  15. Best in Class: Criterion 10Reasonability of Parameters • ODP on PL40: surprising increase in accident parameter in last period

  16. Best in Class: Criterion 11Consistency with Simulation • Murphy on PL10: pick the real data…

  17. Best in Class: Criterion 18Parsimony (Ockham’s Razor) • ODP on IL10: 18 parameters can be reduced to 6 with little loss of fit

  18. Fit For Purpose: Criterion 4Cost/Benefit • Caveats: small sample of data, personal opinion • ER: low benefit • ODP, Mack & Murphy: moderate benefit • More parsimonious models: higher benefit • More data and more models should be evaluated!!!

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