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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

Section 5. Compare, Contrast and Discuss Results

Dr Julie A Sims

Casualty Loss Reserve SeminarBoston, MASeptember 13, 2005

and the winner is

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
more limited aim
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
3 star modelling process
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

fit for purpose criterion 1 aims of the analysis
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
fit for purpose criterion 4 cost benefit
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
adequate fit criterion 14 distributional assumptions
Adequate Fit: Criterion 14 Distributional Assumptions
  • Essential if you want percentiles
  • ER, Mack & ODP: no distribution
  • Murphy on IL40: poor normality = poor fit
adequate fit criterion 15 residual patterns
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
adequate fit criterion 15 residual patterns1
Adequate Fit: Criterion 15Residual Patterns
  • Murphy on IL40: residuals trend up in later accident periods, forecast means likely to be too low
adequate fit criterion 15 residual patterns2
Adequate Fit: Criterion 15Residual Patterns
  • ODP on PL40: residuals trend up and down over calendar periods, forecast means might be high or low
best in class 11 criteria
Best in Class: 11 Criteria!
  • No surprising behaviour
  • Parsimony - as few parameters as is consistent with good fit
best in class criterion 5 cv decreases in later accident periods
Best in Class: Criterion 5CV Decreases in Later Accident Periods
  • ER on PL40: surprising increases in coefficient of variation of accident totals
best in class criterion 10 reasonability of parameters
Best in Class: Criterion 10Reasonability of Parameters
  • ODP on PL40: surprising increase in accident parameter in last period
best in class criterion 11 consistency with simulation
Best in Class: Criterion 11Consistency with Simulation
  • Murphy on PL10: pick the real data…
best in class criterion 18 parsimony ockham s razor
Best in Class: Criterion 18Parsimony (Ockham’s Razor)
  • ODP on IL10: 18 parameters can be reduced to 6 with little loss of fit
fit for purpose criterion 4 cost benefit1
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!!!