Math 479 / 568
Casualty Actuarial Mathematics
Fall 2014
University of Illinois at Urbana-Champaign
Professor Rick Gorvett
Session 4: Loss Reserving I
September 4, 2014
1
Agenda
• Purpose of Loss Reserving
• Loss data
• Types of reserves
• Key dates
• Types of data
• Reserving issues
• The basic loss development technique
2
Purpose of Loss Reserving
• To determine the loss reserve, as of a certain
date, associated with claims incurred by the
insurance company on or prior to that date
– Claims incurred on earned premium
– Balance sheet impact
• Biggest liability item for insurance companies
• Larger reserve  smaller surplus (equity)
– Income statement impact
3
Loss Data
• Types of loss data
–
–
–
–
Paid losses
Incurred losses
Allocated loss adjustment expenses (ALAE)
Other expenses
• Basis of loss data
–
–
–
–
Accident year
Policy year
Calendar year
Report year
4
Types of Reserves
• Provisions for claim obligations associated
with:
–
–
–
–
–
Case reserves
Future development on known claims
Re-opened claims
Incurred but not reported (IBNR)
Reported but not yet recorded
5
Key Dates in the Life of a Claim
• Accident date
• Report date
• Activity dates
– Reserve set up or changed
– Payments made
• Closed date
• Re-opened date (occasionally)
6
Types of Data for Loss Reserving
• Type of data used can vary with the reserving
technique
• Loss development triangles are the traditional
context within which loss reserves are
estimated and analyzed
• General description of process
– Accident / policy year losses at sequential
valuation dates
– Age to age factors (link ratios)
– To-ultimate loss development factors
7
Types of Data (cont.)
• Types of loss data analyzed
– Case incurred losses (and possibly ALAE or even
LAE)
– Paid losses
• For both: cumulative versus incremental
– Claim counts
• Paid versus reported
• Cumulative versus incremental
– Average claim size (severities)
• Paid versus incurred
• Open versus closed claims
8
Reserving Issues
•
•
•
•
Availability of data
Volume of data
How to treat large losses
Other data anomalies – including possible
errors!
• Line of business
• Claim handling procedures
– Reserving philosophies
– Payment philosophies
• Underwriting considerations
• Legal / judicial climate
9
The Basic Loss Development Technique
• Loss development method
– Accident year
– Policy year
– Note: loss development techniques can be
performed on any or all of the following (and
more) bases:
• Paid losses
• Case incurred losses
• Frequency (claim counts) and severity (average claim
size)
10
Paid Loss Development Triangle
Accident
Year
12
2002
2003
2004
2005
2006
100
140
200
250
290
Maturity (months)
24
36
48
190
290
410
500
300
420
600
362
500
60
380
11
Age-to-Age Development Factors
(Link Ratios)
Accident
Year
12-24
24-36
36-48
48-60
60-Ult.
2002
2003
2004
2005
1.900
2.071
2.050
2.000
1.579
1.448
1.463
1.207
1.190
1.050
Average
2.005
1.497
1.199
1.050
Selected
2.000
1.500
1.200
1.050
1.000
12-Ult.
24-Ult.
36-Ult.
48-Ult.
60-Ult.
3.780
1.890
1.260
1.050
1.000
To-Ult.
12
Projection of Ultimate Losses and
Loss Reserves
Accident
Year
Loss @
12/06
2002
2003
2004
2005
2006
380
500
600
500
290
=====
2,270
Total
Projected
Ultimate
LDF
Loss
1.000
1.050
1.260
1.890
3.780
380
525
756
945
1,096
=====
3,702
Projected
Loss
Reserve
25
156
445
806
=====
1,432
13
General Loss Development Approach
• Loss development triangle
• Age-to-age factors (link ratios)
– Approaches to selecting factors – e.g.,
•
•
•
•
Straight average
Average of last three years
(Middle) 3 of 5 years
Weighted average (by dollars)
• To-ultimate loss development factors
• For each (accident) year: (actual loss) ×
(LDF) = estimated ultimate loss
• Reserve = (ultimate loss) – (to-date paid loss)
• IBNR (broad def’n.) = (ultimate loss) – (case 14
incurred loss)
CAS Exam 6, Fall 2007, #7
15
CAS Exam 6, Fall 2008, #9a
16
CAS Exam 6, Spring 2004, #2
17
Next Time
• Loss Reserving II
• Other techniques
• Chapter 5 of Foundations of Casualty
Actuarial Science
18