Enhanced GLMs and vehicle grouping

9 downloads 1095 Views 10MB Size Report
... for thought – carefully constructed manual factor combinations can also yield material benefits .... LOOK. 0. 5. LOOK. 5. FIAT PUNTO 75 SX. FIAT PUNTO 75.
E2: Enhanced GLMs and vehicle grouping

Duncan Anderson & Sami Abdel-Gadir EMB

© 2010 The Actuarial Profession y www.actuaries.org.uk

0

Agenda g

Enhanced GLMs

and vehicle grouping

Duncan Anderson

Sami Abdel-Gadir

© 2010 The Actuarial Profession y www.actuaries.org.uk

1

Interactions 1.7

1.5

1.3

1.1

0.9

0.7

0.5

16

17

18

19

20

21

22

23

24

25

26

27 28 29 30 31 Policyholder Age

32

33

34

40-44 50-54 60-64 70+ 35-39 45-49 55-59 65-69

2

Interactions 5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5 16

17

18

19

20

21

22

23

24

25

26

27 28 29 30 Policyholder Age

31

32

33

34

40-44 35-39

45-49

70+ 50-54 60-64 55-59 65-69

3

Interactions 1.2

55%

1.1

50%

1.0

45%

0.9

40%

0.8

35%

0.7

30%

0.6

25%

0.5

20%

0.4

15%

0.3

10%

0.2

5%

0.1

0%

Policyholder Age

4

Why y are interactions p present?

– Because that's how the factors behave – Because the multiplicative model can go wrong at the edges – 1.5 * 1.4 * 1.7 * 1.5 * 1.8 * 1.5 * 1.8 = 26!

5

Interactions

Vehicle group β β − β β β β β β β

Age

Vehicle group

Vehicle group

β β − β β β β β β β

β β − β β β β β β β

β

− − − − − − − − − −

β

β β − β β β β β β β

β

− − − − − − − − − −

β

− − − − − − − − − −

β

β β − β β β β β β β

β

− − − − − − − − − −

β

− − − − − − − − − −

β

β β − β β β β β β β

β

− − − − − − − − − −



− − − − − − − − − −



− − − − − − − − − −



− − − − − − − − − −

β

− − − − − − − − − −

β

β β − β β β β β β β

β

− − − − − − − − − −

β

− − − − − − − − − −

β

β β − β β β β β β β

β

− − − − −

β

− − − − − − − − − −

β

β β − β β β β β β β

β

− − − − −

β β β

− − − − − − − − − − − − − − − − − − − − − − − − − − − − − −

β β β

β β − β β β β β β β β β − β β β β β β β β β − β β β β β β β

β β β

− − − − − − − − − − − − − − −

Age

Age

β

6

Example p

Example p

Example p

Saddles

Saddles

Saddles

Saddles

Saddles

Saddles

Saddles

Saddles

Saddles

Saddles

Saddles

Saddles - model comparison p Motor frequency - out of sample 20%

400 000 400,000

18%

350,000

16%

300,000

14%

250,000

12%

200,000

10%

150,000

8%

100,000

6%

50,000

4%

0 50%

70%

90%

94%

98% Exposure

102% Saddle

106% Original

110%

130%

150%

22

Saddles - model comparison p Motor frequency - out of sample 20%

400 000 400,000

18%

350,000

16%

300,000

14%

250,000

12%

200,000

10%

150,000

8%

100,000

6%

50,000

4%

0 50%

70%

90%

94% Exposure

98%

102% Observed

106% Saddle

110% Original

130%

150%

23

Saddles - model comparison p Motor frequency - out of sample 2.6%

900000

2.4%

800000

2.2% 700000

2.0% 600000

1.8% 500000 1.6% 400000 1.4%

300000 1.2%

200000 10% 1 .0%

100000

0.8%

0 6% 0.6%

0 < 80%

80% 86%

83% 89%

86% 92%

89% 95%

92% 98%

95% 101%

98% 104%

Exposure

101% 107%

104% 110%

Observed

107% 113%

110% 116%

Saddle

113% 119%

116% 122%

Original

119% 125%

122% 128%

125% 131%

128% 134%

> 130%

24

Saddles - model comparison p Motor frequency - out of time 1000000

0.026

900000

800000

700000 0.021

600000

500000 0.016 400000

300000

0.011 200000

100000

0.006

0 < 80%

80% 84%

82% 86%

84% 88%

86% 90%

88% 92%

90% 94%

92% 96%

94% 98%

96% 100%

98% 102%

100% - 102% - 104% - 106% 104% 106% 108% 110%

Exposure

Observed

108% 112%

Saddles

110% 114%

112% 116%

114% 118%

Original

116% 120%

118% - > 120% 122%

25

Saddles - model comparison p Motor renewals - out of sample 0.4

14000

0.35

12000

10000 0.3

8000

0.25

6000

4000

02 0.2

2000

0 15 0.1

0 < 80%

80% - 86%

83% - 89%

86% - 92%

89% - 95%

92% - 98%

Exposure

95% - 101%

Observed

98% - 104% 101% - 107% 104% - 110% 107% - 113% 110% - 116%

Saddles

Original

113% - 119% 116% - 122%

26

Machine vs man

vs

27

Machine vs man

vs

28

Machine vs man

What is the underlying process?

29

Machine vs man

What are the underlying drivers?

30

Machine vs man

What segments can I dream up? Y Young mothers th with ith 4x4s 4 4 doing d i the school run Old people l driving di i a Honda H d Jazz J going slowly in front of me

31

Key y messages g

– “Saddle” method of interaction detection can identify many subtle interactions and yyield materiallyy more p predictive models – This is no replacement for thought – carefully constructed manual factor combinations can also yield material benefits

32

Agenda g

Enhanced GLMs

and vehicle grouping

Duncan Anderson

Sami Abdel-Gadir

33

The starting g point p – the ABI 50 vehicle classification



New vehicles classified according to: – Damage and parts costs – Repair times – New car values – Performance – Security



50 groups in use plus suffixes



Imported cars and specialised purpose vehicles e e.g. g kit cars are not classified



For details see: http://www.thatcham.org/abigrouprating/index.jsp?page=429 34

How g good is ABI 50 for risk models and pricing? p g •

Useful benchmark

Proportion of TPBI and TPPD Burning Cost - market measure 100% 90%



Public awareness

80% 70%



Very good predictor of total loss?

60% 50%

• •

Good predictor of claim frequency? Better predictor of AD claims experience than TP?

40% 30% 20% 10% 0% 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

TPBI

TPPD

Other

But... Ford Mondeo Zetec

7%



does not acknowledge all vehicle attributes

Citroen C1 Cool

6%

5%



does not make full use of the 50 groups

% of Cars

Porsche Boxster S 4%

3%

2%

1%

49

47

45

41

43

39

37

35

31

33

27

ABI 50

29

23

25

21

19

17

13

15

9

11

5

7

0%

3

is a one-size fits all vehicle group th b the bestt option? ti ?

1



35

Insurer classifications

36

Postcoding g - framework

Standard Policy F t Factors

Random Noise

External Geographical Factors

Residual R id l Spatial Variation

37

Spatial p smoothing g

– Credibility family method – Can adopt distance based or adjacency based approach

Unsmoothed

Residual Spatial Variation

Distance

Adjacency

Smoothed 38

Car classification – translating g the framework

Standard Policy F t Factors

Random Noise

External Vehicle Factors

Residual R id l Spatial Variation

39

Back to basics

Dimensions

Body style

Safety

Performance

Security

Cost

Brand Appeal

Use 40

Body y style y classification It’s hard! – No universally adopted system in place – Many variants to classify – New bodystyles have emerged – Some vehicles attempt to defy classification Hatchback

Cabriolet

Spider

Saloon 41

Car classification – translating g the framework

External Vehicle Factors Performance Di Dimensions i Safety Security Costs Bodystyle Classification

Standard Policy Factors

Random Noise

Residual Spatial Variation

Vehicle Weight Exposure

TPPD Frequency

42

Car classification – translating g the framework

Residual Spatial Variation Standard Policy Factors

Random Noise

Unsmoothed

Smoothed

Requires q a vehicle space... p

External Vehicle Factors

43

Example p adjacencies j

0

PEUGEOT 206 PEUGEOT 206 ZEST STY LE ZEST STYLE

VOLKSWAGEN VOLKSWAGEN POLO E SDI POLO E SDI

5

0

5

PEUGEOT 206 PEUGEOT 206 LOOK LOOK

0

5

FIAT PUNTO 75 FIAT PUNTO 75 SX SX

0

TOYOTA YARIS TOYOTA YARIS L ZINC D-4D L ZINC D-4D 5

44

Putting g it all together g Classifying existing cars

Length

49

46

43

40

37

34

31

28

22

25

19

16

13

7

10

4

Relativity

1

Exposure

Vehicle Group

Classifying new cars BHP Exposure

1

2

3

4

5

Relativity

6

7

8

9

10

Smoothing Band

Exposure

Smoothing Adjustment

45

0. 0.7 1 73 -0 . 0. 76 7 4 -0 0. .7 7 79 0. - 0. 8 82 -0 . 0. 85 8 3 -0 . 0. 88 8 6 0. 0.8 9 91 0. 0.9 94 2 -0 . 0. 97 9 5 -0 .9 8 1 -1 .0 1. 1 03 -1 1. . 06 0 4 -1 1. .0 7 09 1. - 1. 1 12 -1 . 1. 15 1 3 1. 1.1 18 6 -1 . 1. 21 1 9 1. 1.2 2 24 -1 . 1. 27 2 5 -1 1. .2 8 3 -1 . 1. 33 31 1. 1.3 4 36 -1 1. .3 7 39 -1 .4

0. 7

Relattivity 1.4 4.0%

1.3 3.5%

1.2 3.0%

1.1 2.5%

1 2 0% 2.0%

0.9 1.5%

0.8 1.0%

0.7 0.5%

0.6 0.0%

% Exposure Actual ABI 50

% Exp posure

Performance vs. ABI (TP) ( )

TP VG / ABI 50

TP VG

46

Key y messages g

– Techniques learned from postcode classification can be successfullyy applied pp to car classification – There are practical challenges around making best use of external data but these can be overcome

47