The Analysis and Estimation of Loss & ALAE Variability

Section 5. Compare, Contrast and Discuss Results

Dr Julie A Sims

Casualty Loss Reserve SeminarBoston, MA

September 13, 2005

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

Data Model

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

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

• 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 14Distributional Assumptions

Murphy on IL40

Adequate Fit: Criterion 14Distributional Assumptions

Murphy on IL40

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 15Residual Patterns

• Murphy on IL40: residuals trend up in later accident periods, forecast means likely to be too low

Adequate Fit: Criterion 15Residual Patterns

• ODP on PL40: residuals trend up and down over calendar periods, forecast means might be high or low

PL40 - Res vs Cal Qtr

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

0 10 20 30 40

Best in Class: 11 Criteria!

• No surprising behaviour• Parsimony - as few parameters as is

consistent with good fit

Best in Class: Criterion 5CV Decreases in Later

Accident Periods• ER on PL40: surprising increases in

coefficient of variation of accident totalsPL40 Future Payment CV

0%20%40%60%80%

100%120%140%160%180%

1994

Q3

1995

Q3

1996

Q3

1997

Q3

1998

Q3

1999

Q3

2000

Q3

2001

Q3

2002

Q3

Tota

l

Accident Quarter

ER cv

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

IL10 - Fitted Values vs Acc Qtr for Dev Qtr 1

0

2000

4000

6000

8000

10000

12000

14000

2001

Q1

2001

Q2

2001

Q3

2001

Q4

2002

Q1

2002

Q2

2002

Q3

2002

Q4

2003

Q1

2003

Q2

10

4

3

Number of accident parameters

IL10 - Fitted Values vs Dev Qtr for Acc Qtr 1Q2001 (log scale)

100

1000

10000

1 2 3 4 5 6 7 8 9 10

8

4

3

Number of development parameters

Fit For Purpose: Criterion 4 Cost/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!!!