The Analysis and Estimation of Loss &amp; ALAE Variability

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The Analysis and Estimation of Loss &amp; 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

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
• 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

Fit for purpose: Criteria 1, 2, 3, 4

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
• 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
• 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
• Essential if you want percentiles
• ER, Mack & ODP: no distribution
• Murphy on IL40: poor normality = poor fit
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
• Murphy on IL40: residuals trend up in later accident periods, forecast means likely to be too low
• ODP on PL40: residuals trend up and down over calendar periods, forecast means might be high or low
Best in Class: 11 Criteria!
• No surprising behaviour
• Parsimony - as few parameters as is consistent with good fit
• ER on PL40: surprising increases in coefficient of variation of accident totals
Best in Class: Criterion 10Reasonability of Parameters
• ODP on PL40: surprising increase in accident parameter in last period
Best in Class: Criterion 11Consistency with Simulation
• Murphy on PL10: pick the real data…
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 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!!!