1 milliman

Motor Pricing Models: Bridging the Gap Between Theory and Reality SOAT Non-Life Insurance Forum 2011

23 September 2011

About Milliman Founded in 1947, with 53 offices worldwide.

Over 120 fully qualified general insurance actuaries, over 120 fully qualified health insurance actuaries, and over 2,400 staff Milliman is the leading provider of actuarial and related products and services to insurance markets worldwide.

Over USD 650 million in consulting revenues Experts by lines of business – Actuaries, underwriters, and claims experts, many with over 20 years’ experience in specific lines of business such as Motor insurance, medical insurance, medical malpractice, mortgage insurance, etc. – For medical insurance alone, Milliman has over 200 dedicated consultants, including doctors, nurses, health IT specialists, and former hospital administrators.

In Asia, Milliman has over 180 staff spread across Tokyo, Seoul, New Delhi, Dubai, Taipei, Hong Kong, Shanghai and Singapore Have worked with over 30 non-life companies in Thailand.

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What is Pricing?

Charging the price that maximises profit Key questions – How much is the customer willing to pay?

– How price sensitive is the customer?

– What are my costs in terms of expenses and expected claims?

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Risk Segmentation / Predictive Modelling No two risks are identical Approaches to risk segmentation – One-way analyses / two-way analyses – Generalised Linear Models – Machine Learning

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One-Way Analysis: Age of Driver Relativities

Burning Costs 12,000

1.4

10,000

1.2

8,000

1

6,000

0.8

4,000

0.6

2,000

0.4

0

0.2 <30

30-34

35-39

<30

30-34

35-39

>=40

>=40

For Honda Civic

One-way Analysis of Age Age

<30

30-34

Burning Cost $ 9,819 $ 7,505 $ 6,254 $ 5,941 Relativities 1.31 1.00 0.83 0.79

5

35-39

>=40

One-Way Analysis: Car Make-Model Relativities

Burning Cost 1.6

12000

1.4

10000

1.2 8000 1 6000

0.8

4000

0.6 0.4

2000

0.2 0 1300CC

1600CC

Type-R

0 1300CC

For Honda Civic

One-way Analysis of Model Model

1300CC

1600CC

Type-R

Burning Cost $ 7,505 $ 8,105 $ 10,882 Relativities 1.00 1.08 1.45 6

1600CC

Type-R

Two-Way Analysis For Honda Civic

One-way Analysis of Age Age

<30

30-34

35-39

>=40

Burning Cost $ 9,819 $ 7,505 $ 6,254 $ 5,941 Relativities 1.31 1.00 0.83 0.79 One-way Analysis of Model Model

1300CC

1600CC

Type-R

Burning Cost $ 7,505 $ 8,105 $ 10,882 Relativities 1.00 1.08 1.45 2-way Analysis Age

<30

30-34

35-39

>=40

1300CC 1600CC Type-R

1.31 1.38 1.55

1.00 1.08 1.45

0.83 0.93 1.18

0.79 0.91 1.08

One-way analysis ignores correlation and interaction between factors 7

GLM GLM is a sophisticated form of curve-fitting

g(Âľ) = b0 + b1X1 + b2X2 + ... + bkXk + ei

Rating factors, e.g., make-model, age of driver, driving experience

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GLM Rating Structure State-of-the-art in the 1970s and 1980s, perhaps even the 1990s – Takes into account correlation between factors – Easy to apply in practice in terms of developing a rating structure Own Damage Private Vehicle

Less than 1 1-2 years year

2-6 years

6+ years

Fixed Fixed Fixed Fixed Rate Rate Rate Rate premi premi premi premi (%) (%) (%) (%) um um um um <6 Seats

539 1.28

513

1.22

508 1.21

523 1.24

6-10 Seats

646 1.28

616

1.22

609 1.21

628 1.24

10+ Seats

646 1.28

616

1.22

609 1.21

628 1.24

Rating Factor Factor Designated C1a 0.9 Driver C1 C1b 1 C2a 1.05 C2b 1 Driver’s Age C2 C2c 0.95 C2d 1 C2e 1.05 Gender C3a 1 C3 C3b 0.95 C4a 1.05 Driving Years C4b 1.02 C4 C4c 1 C5a 1 Pre-defined Driving Area C5b 0.95 C5 C5c 0.92 C6a 0.9 Average Annual C6b 1 Mileage C6 C6c 1.1-1.3 Traffic Violation Record C8

9

C8a

0.9

C8b

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Description With designated driver Undesignated driver Younger than 25 years old [25,30) [30,40) [40,60) At least 60 years old Male Female Less than 1 year [1,3) At least 3 years Domestic Within province Routine lLess than 30,000 km/p.a.

[30000,50000) km/p.a.

At least 50,000 km/p.a.

No liable traffic ticket record in previous year Liable traffic ticket record (s) in previous year

GLM Curve fitting smooths the data â&#x20AC;&#x201C; Eliminates volatility in claims experience; can be powerful if the model fits Claim Size Distribution and Lognormal Regression

Simple Linear Regression 0 1.20

0.030

1.00

0.025

5000

10000

15000

25000 0.03 0.03

Log Normal

Empirical

0.80

0.020

0.02

0.60

0.015

0.02

0.40

0.010

0.01

0.20

0.005

0.01

-

0.000

-

-

10

5

10

Make

15

20

25

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169 177 185 193

Relativities

20000

GLM Results: Does the Curve Fit? Empirical Experience 1.4

1.3

Relativities

1.2 6+ Years 1.1 Less than 6 1

0.9

0.8 Less than 24

11

25-29

30-34

35-39

40-44

45-49

Driverâ&#x20AC;&#x2122;s Age

50-54

55-59

60-64

65+

GLM Results: Does the Curve Fit? GLM output 1.4

1.3

Relativities

1.2 6+ Years 1.1 Less than 6 1.0

0.9

0.8 Less than 24

25-29

30-34

35-39

40-44

45-49

Driverâ&#x20AC;&#x2122;s Age

12

50-54

55-59

60-64

65+

Are the Results Credible?

GLM Output_Make/Model 1.8 Est

95% Confidence Interval

1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0.9 1

13

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

United Kingdom Gross U/W Margin

10% 5% 0% 1985 -5% -10% -15% -20% -25%

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1990

1995

2000

2005

Machine Learning Addresses the fundamental questions directly – Where are we making money? Where are we losing money?

– Can we be confident?

Identifies risk segments that are credible and produce consistent results from year to year – Iterative, artificial intelligence process – User defines the degree of credibility within segments Results are only as good as the algorithm – A good algorithm will maximise the number of segments identified

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Too Complicated!

Renewal 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1

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Vehicle age 7 5 9 10 8 3 4 5 5 4 9 10 2 2 9 8 4 8 2 2 4 3 2 9 9 3 4 8

SI_OD 1_0-40 C 1_0-40 C 3_80-120 C 6_300+ C 1_0-40 C 1_0-40 C 1_0-40 C 1_0-40 C 3_80-120 C 4_120-180 C 2_40-80 C 6_300+ C 6_300+ C 6_300+ C 1_0-40 C 4_120-180 C 1_0-40 C 3_80-120 C 1_0-40 C 1_0-40 C 5_180-300 C 2_40-80 C 5_180-300 C 2_40-80 C 2_40-80 C 3_80-120 C 4_120-180 C 2_40-80 C

L_SI2 200 200 40 300 120 300 80 300 200 200 40 40 300 40 40 80 80 250 40 200 200 300 250 300 80 250 80 300

brand

channel

coverage

Dpt

NCD

HONDA BMW AUDI PASSAT GM HONDA TOYOTA AUDI GM BORA POLO HYUNDAI JETTA NISSAN VW TOYOTA VW TOYOTA BENZ MAZDA GMC BMW FORD MAZDA BUICK BENZ AUDI BUICK

A B A B C None None None None None B None None A B None A A A None None None C None None None None None

Base_Rider Comprehensive Comprehensive Comprehensive Comprehensive Base_Rider Base_Rider Comprehensive Comprehensive No_Rider Base_Rider Comprehensive Comprehensive Comprehensive Base_Rider Base_Rider Base_Rider Comprehensive Comprehensive Base_Rider Base_Rider No_Rider Base_Rider Base_Rider Base_Rider Base_Rider Base_Rider Base_Rider

A A A A A A B A A B A A C A A A A A A A B C A C B C C B

Y N Y N Y N N Y Y N Y Y N N Y N N N N N Y N N N Y Y N N

Driver # of Safety Gender Age Drivers 48 Y 2 M 61 N 1 M 52 N 2 F 24 Y 1 M 67 N 3 F 25 Y 1 M 19 N 1 F 41 Y 3 F 52 Y 1 F 61 Y 2 M 62 N 1 M 58 Y 1 M 21 N 4 F 27 N 1 M 30 Y 2 M 74 Y 5 M 16 Y 2 F 53 N 1 M 51 Y 2 M 50 N 1 F 70 N 3 M 37 N 1 M 19 N 5 M 21 Y 1 F 20 Y 2 M 56 N 1 M 60 N 1 M 41 Y 1 M

LR1

LR2

LR3

85.0% 12.6% 0.0% 0.0% 75.0% 17.4% 25.0% 43.6% 76.5% 44.8% 13.6% 0.0% 57.5% 0.0% 63.2% 0.0% 0.0% 12.8% 17.2% 14.9% 44.9% 70.6% 0.0% 0.0% 95.0% 49.4% 16.2% 19.7%

49.3% 125.0% 49.2% 59.7% 37.4% 46.0% 51.4% 0.0% 0.0% 25.0% 93.2% 0.0% 58.9% 80.8% 37.2% 0.0% 0.0% 13.2% 31.8% 32.3% 27.8% 0.0% 0.0% 37.5% 1.5% 56.5% 0.0% 24.0% 90.0% 120.0% 0.0% 82.4% 0.0% 0.0% 37.7% 42.6% 25.2% 88.1% 45.9% 37.9% 0.0% 26.1% 79.2% 43.3% 89.0% 41.0% 51.8% 47.3% 73.5% 85.0% 9.4% 10.0% 91.6% 73.2% 0.0% 0.0%

Insight Customer Segment Example

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Customer Segments are Defined by “Significant Attributes” (Compound Variables) Loss Ratio = 120%

Loss Ratio = 35% No

Yes

65%

70%

NCD

Safety Devices

AND < 50

50+

78%

60%

Age

74%

Legend

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%

Univariate Loss Ratios

%

Attribute Combination Loss Ratios

58%

1+

62%

83%

Female

Male

66%

75%

Age Safety Devices

74%

< 50

No 58%

No

1

AND Yes

Yes

78%

< 6 years

6+ years

75%

69%

Number of Drivers

Driver’s Gender 50+ 60% Vehicle Age

Analysis of Anti-Selection 4 Best Performing Segments • 15% of the Exp., • 21% of the Premium • 15% of their Claims

4 Worst Performing Segments • 13% of the Exp., • 9% of the Premium • 15% of their Claims

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Technology/Modern Statistical Techniques Make The Difference…

Current Methods

Machine Learning

•

Assumes that variables are independent

•

No underlying curve-fitting model or assumptions

•

User needs to discover interactions between variables through trial and error

•

Does not require the user to specify the predictors and interactions to be included in the model - it discovers them

•

Interactions and rating structure applied uniformly across the model.

•

Segments based on credibility, not by a fixed format. “Data Speaks For Itself”

•

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GLM produces a convenient rating structure. Machine Learning helps to expose weaknesses in the structure, so that the structure and underwriting guidelines may be refined