Claims Applications of GLM

Rob Walling

CAS GLM Seminar

October 4, 2004

Overview

What types of claims are most applicable? What factors matter? Why does GLM help?

Basic Formula Case Reserving Model

BOP Property Losses– Initial Case Reserve at First Report

Water Claims - $2,500 Wind/Hail claims - $5,000 All Others - $1,700 Large Property Losses initially set at $25,000

– Annual Adjustments for Trends

Suitable Claim Types

Large Volume of Claims Less Variability in Severities Known Factors Differentiate Severities

Suitable Claim Types - Commercial

Non-Severe Property Claims Commercial Auto Physical Damage Commercial Auto Property Damage Commercial Auto PIP General Liability Property Damage OL&T Minor Bodily Injury Workers Compensation Medical Workers Compensation Temporary Total and

Minor Permanent Partials Products Liability???

Factors that Impact Severities

Geography (State or Regional Courts) Time (Inflation, Settlement Lags) Claimant Characteristics (Age, Class) Insured Characteristics (Vehicle Weight) Attorney Involvement Preferred Claim Network (Medical, Glass,

Auto Repair, Attorney) Other Claims Features (Arbitration)

Medical Malpractice Claims Severities

Predicted Values

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

1,000,000

Occ_Year

SEV_DESC (DEATH)

SEV_DESC (Emotional Only - Fright, no physical damage)

SEV_DESC (Permanent: Major -Paraplegia, blindness, loss of twolimbs, brain damage.)

SEV_DESC (Permanent: Minor -Loss of fingers, loss or damage to organs. Includes non-disabling injuries.)

SEV_DESC (Permanent: S ignificant - Deafness, loss of limb, loss of eye, loss of one kidney or lung.)

SEV_DESC (Temporary: Major - Burns, surgical material left, drug side effect, brain damage. Recovery delayed.)

SEV_DESC (Temporary: Minor - Infections, misset fracture, fall in hospital. Recovery delayed.)

SEV_DESC (Temporary: S light -Lacerations, contusions, minor scars, rash. No delay.)

Claim Severity by Injury Type Over Time

Severity Trends – Occurrence YearPredicted Values

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

0%

2%

4%

6%

8%

10%

12%

14%

Occ_Year

Severities by Settlement LagPredicted Values

0

10,000

20,000

30,000

40,000

50,000

60,000

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Settlement_Lag

Differences by Age & SexPredicted Values

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

10 20 30 40 50 60 70 80

IP_Age

IP_Sex (F)

IP_Sex (M)

Weight - Property Damage

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

2.000

Weight (100's)

Rel

ativ

ity

Relative Pure Premium

Weight - Collision

0.000

0.200

0.400

0.600

0.800

1.000

1.200

Weight (100's)

Rel

ativ

ity

Relative Pure Premium

Collision Vehicle Classification AnalysisRun 1 Model 2 - Model with All Variables - Collision Severity

23%

3%

-1%

6%

3%

11%

0%

1%

3%

-2%

-4%

1%

-1%

-4%

-1%

-0.21

-0.14

-0.07

0

0.07

0.14

0.21

0.28

engine displacement

Log

of m

ultip

lier

0

5000

10000

15000

20000

25000

Num

ber o

f cla

ims

Approx 95% confidence interval Unsmoothed estimate Smoothed estimate

Predicted Values

-1000

1000

3000

5000

7000

9000

11000

0 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25

HIGHINJ

0

50

100

150

200

250

300

ATTORNEY (3) Exposure

ATTORNEY (2) Exposure

ATTORNEY (1) Exposure

ATTORNEY (2)

ATTORNEY (1)

Impact of Attorney Involvement on Claim Severity

Profiles by Resolution MethodPredicted Values

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

0%

20%

40%

60%

80%

100%

120%

140%

160%

Disposed of by Arbitration Disposed of by Court NO RESPONSE SETTLED BY PARTIES

FIN_METH_DESC

Typical Causes of Loss

Property– Fire & Lightning– Windstorm & Hail– Water Damage – Burglary & Theft– Inland Marine

Liability– Bodily Injury– Medical Payments– Property Damage

Typical Causes of Loss

Workers Compensation– Medical– Temporary Total– Minor Permanent Partial

Liability– Bodily Injury– Medical Payments– Property Damage

Severities By Claim TypePredicted Values

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

DEATH Emotional Only -Fright, no physical

damage

NO RESPONSE Permanent: Grave -Quadraplegia,severe brain

damage, lifelongcare or fatalprognosis.

Permanent: Major -Paraplegia,

blindness, loss oftwo limbs, brain

damage.

Permanent: Minor -Loss of fingers,

loss or damage toorgans. Includes

non-disablinginjuries.

Permanent:S ignificant -

Deafness, loss oflimb, loss of eye,loss of one kidney

or lung.

Temporary: Major -Burns, surgicalmaterial left, drugside effect, brain

damage. Recoverydelayed.

Temporary: Minor -Infections, misset

fracture, fall inhospital. Recovery

delayed.

Temporary: S light -Lacerations,

contusions, minorscars, rash. No

delay.

SEV_DESC

Why Use GLM for Formula Case Reserves?

Interactions Matter Allows Testing of Trends and Stability Over

Time Measures Variability in Severities

Predicted Values

-1000

1000

3000

5000

7000

9000

11000

0 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25

HIGHINJ

0

50

100

150

200

250

300

ATTORNEY (3) Exposure

ATTORNEY (2) Exposure

ATTORNEY (1) Exposure

ATTORNEY (2)

ATTORNEY (1)

Impact of Attorney Involvement on Claim Severity

3.0 5.1 3.98.1

10.812.1

38.0

25.1 26.121.7

9.814.4

8.3

13.6

0

10

20

30

40

Per

cent

age

16-20 21-25 26-30 31-40 41-50 51-60 61+

Age

Interaction with Rick Characteristics:Minivan Drivers by Age

Minivan Non-Minivan

Sample Homeowners AnalysisRun 1 Model 2 - Homeowners Score Every Year - Claim Severity

9%

4%

-9%-11%

-5%

-21%

0%

42%

-14%

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

protection class

Log

of m

ultip

lier

0

500

1000

1500

2000

2500

3000

3500

4000

1 2 3 4 5 6 7-8 9-10 <missing> & 00

Num

ber

of c

laim

s

Approx 95% confidence interval Unsmoothed estimate Smoothed estimate

Severities by Protection Class

Incurred % of Ultimate Paid by Age Strata from First Report

0.7

0.75

0.8

0.85

0.9

0.95

1

Jan-03 Feb-03 Mar-03 Apr-03 May-03 Jun-03 Jul-03 Aug-03 Sep-03 Oct-03 Nov-03 Dec-03 Jan-04 Feb-04 Mar-04 Apr-04 May-04 Jun-04 Jul-04

First Close Year/Month - Rolling 12 MonthsIncurred 90 Day from Open % of Ultimate Paid Incurred 180 Day from Open % of Ultimate Paid Incurred 360 Day from Open % of Ultimate Paid

Other Claims Applications

Benchmarking of Claims Offices Evaluation of External Claim Service

Providers Impact of Defense Costs by Claim Type

ALAE / Loss+ALAE by Settlement LagPredicted Values

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Settlement_Lag

Non-Economic Damages by Occurrence YearPredicted Values

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0%

2%

4%

6%

8%

10%

12%

14%

Occ_Year