Post on 21-Jan-2016
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