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Measuring Claims Inflation: an Argentinean Case Study
Frank Cuypers
2
Motor Liability in Argentina
closed without indemnity
closed with indemnity
closed without indemnity
closed with sentence
closed with settlement
ADMINISTRATIVE
MEDIATION
TRIAL
CLAIM
closed without indemnity
closed with indemnity
Homogeneous portfolio ≠ homogeneous claims
Claims type segmentation Material damage (RCC) Bodily injury (RCL) Death (RCHO)
Claims legal segmentation Administrative (ADM) Mediation (MED) Trial (TRI)
3
Claims Durations
Long tail business
Little IBNYR
0%
20%
40%
60%
80%
100%
120%
0 5 10 15
RCL TRIRCL MEDRCHO TRIRCHO MEDRCC TRIRCC MEDall ADM
0%
20%
40%
60%
80%
100%
120%
140%
160%
0 5 10 15
RCL TRIRCL MEDRCHO TRIRCHO MEDRCC TRIRCC MEDall ADM
4
Claims Timing
Payout mostly at settlement Lump sum + expenses No medical treatments No annuities
0-6 months
time
clai
m p
ayou
t
LAE
indemnity + LAE
5
Claims Timing
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-1 0 1 2 3 4 5 6 7 8 9 10 11 12
exce
edan
ce p
roba
bilit
y
month
all
2'013
2'012
2'011
2'010
2'009
2'008
2'007
1
2
3
4
5
6
7
6
Claims Timing
Payout mostly at settlement Lump sum + expenses No medical treatments No annuities
Define a claims „mortality“ table:
𝑞𝑞𝑥𝑥 → Γ𝑠𝑠|𝑛𝑛 = probabilityto settle in year 𝑠𝑠if still open in year 𝑛𝑛 ≤ 𝑠𝑠
0-6 months
time
clai
m p
ayou
t
LAE
indemnity + LAE
7
Claims Reserves
Statutory reserves Strict prescribed mechanic procedure⇒ Useless
ALAE Individualy volatile Stable on average
8
Claims Predictor: Plaintiff‘s Demand
Nearly independent from indemnity⇒ Useless
0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%
inde
mni
ty
demand
0
10'000
20'000
30'000
40'000
50'000
60'000
70'000
80'000
90'000
100'000
0 500'000 1'000'000
inde
mni
ty
demand
9
Claims Predictor: Disability Points
Only for bodily injury (physical + psychological) Volatile Average nearly proportional to indemnity Awarded points increase with claim‘s duration
Forensic physicians fees proportionate to indemnity!
0
1'000
2'000
3'000
4'000
5'000
6'000
7'000
8'000
9'000
10'000
0 20 40 60 80 100
inde
mni
ty p
er p
oint
disability points
MEDTRI
0
1'000
2'000
3'000
4'000
5'000
6'000
7'000
8'000
9'000
10'000
0 20 40 60 80 100
inde
mni
ty p
er p
oint
disability points
MEDTRI
10
Claims Inflation
Which inflation?
Government statistics Falsified
Commercial statistics Numerous Inconsistent
0.1
1.0
1'998 2'003 2'008 2'013calendar year
wages 1 wages 2
CPI 1 CPI 2
casco parts
11
Claims Interests
Granted by courts Passive = if plaintiff wealthy Active = if plaintiff must borrow
In-between interests exist
Accounted for in settlements But inconsistently
Not compounded!
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
1'991 1'996 2'001 2'006 2'011calendar year
active interest
passive interest
12
Claims Procrastination
Complex claims take longer
Procrastination increases indemnity Lawyers fees Forensic physicians Award of psychological disability points …
Adds up de facto to the effect of claims interests:
The longer it takes a claim to settle, the higher the indemnity
13
Claims Normalization
Hypothesis: Interest & procrastenation
independent of settlement year Inflation independent of duration
⇒ Normalize indemnities to compare claims:
𝑋𝑋 → �𝑋𝑋 = Λ𝑛𝑛𝑠𝑠 Π𝑎𝑎𝑠𝑠 𝑋𝑋
Π Λ
sa n t
inflation interests & procrastination
settl
emen
tyea
r
development year0 1 2 3 4 5 6 7
2006
2007
2008
2009
2010
2011
2012
2013
same inflation
same interests& procrastination
14
Inflation
Normalize indemnities To current callendar year Kolmogorov-Smirnov fit
Indemnities survival probabilities Different scales according to accident year Similar lognormal shape
SY 2 as-is SY 2 as-if
0.1%
1.0%
10.0%
100.0%
1'000 10'000 100'000 1'000'000indemnity amount
2'0132'0122'0112'0102'0092'0082'0072'006lognormal
0.1%
1.0%
10.0%
100.0%
1'000 10'000 100'000 1'000'000indemnity amount
2'0132'0122'0112'0102'0092'0082'0072'006lognormal
0.1
1.0
2'005 2'007 2'009 2'011 2'013settlement year
15
Inflation
settl
emen
tyye
area
r
development year0 1 2 3 4 5 6 7
2006
2007
2008
2009
2010
2011
2012
2013
inflation vector
0.1
1.0
2'005 2'007 2'009 2'011 2'013settlement year
16
Inflation
0.1
1.0
2'005 2'007 2'009 2'011 2'013settlement year
RCC used
RCC 0
RCC 1
RCC 2
RCC 3
settl
emen
tyye
area
r
development year0 1 2 3 4 5 6 7
2006
2007
2008
2009
2010
2011
2012
2013
same constant inflation vectors
17
Inflation
2 different claims inflations RCC material damage & death RCL bodily injury
Claims normalization𝑋𝑋 → �𝑋𝑋 = Λ𝑛𝑛𝑠𝑠 Π𝑎𝑎𝑠𝑠 𝑋𝑋
RCCΛ𝑛𝑛𝑠𝑠 = 1 + 20% 𝑛𝑛−𝑠𝑠
RCLΛ𝑛𝑛𝑠𝑠 = 1 + 10% 𝑛𝑛−𝑠𝑠0.1
1.0
2'005 2'007 2'009 2'011 2'013settlement year
RCL usedRCL 0RCL 1RCL 2RCL 3RCC usedRCC 0RCC 1RCC 2RCC 3
Π Λ
sa n t
18
Interests & Procrastination
Normalize indemnities To settlement year 0 Kolmogorov-Smirnov fit
0.1%
1.0%
10.0%
100.0%
1'000 10'000 100'000 1'000'000indemnity amount
01234567lognormal
AY 2006 as-is
0.5
5.0
0 1 2 3 4 5 6 7 8development yearIndemnities survival probabilities
Different scales according to settlement year Similar lognormal shape
0.1%
1.0%
10.0%
100.0%
1'000 10'000 100'000 1'000'000indemnity amount
01234567lognormal
AY 2006 as-if
19
Interests & Procrastination
Claims normalization𝑋𝑋 → �𝑋𝑋 = Λ𝑛𝑛𝑠𝑠 Π𝑎𝑎𝑠𝑠 𝑋𝑋
Π𝑛𝑛𝑠𝑠 = 1 + 20% 𝑎𝑎−𝑠𝑠
settl
emen
tyye
area
r
development year0 1 2 3 4 5 6 7
2006
2007
2008
2009
2010
2011
2012
2013
same interests& procrastination
0.5
5.0
0 1 2 3 4 5 6 7 8development year
used2'0132'0122'0112'0102'0092'008
Π Λ
sa n t
20
Large Claims
Whatever AY, SY, DY Good fit to lognormal No need to separate attritional & large claims
0.1%
1.0%
10.0%
100.0%
1'000 10'000 100'000 1'000'000indemnity amount
01234567lognormal
21
Reserves
past & future interests + procrastination
accidenttime
closurenotification now
future inflation
past interests + procrastination
accidenttime
nownotification closure
past inflation
as-is → as-if
current → ultimate
22
Models
Runoff Exposure Decay Disability LD BF …
23
Models
Runoff Exposure Decay Disability LD BF …
24
Models & Assumptions
Runoff Exposure Decay Disability LD BF …
Policy limits
ALAE
Payout timing
Procrastination
Disability points
Case reserves
…
25
Model: Runoff
Runoff
𝑅𝑅𝑎𝑎 = 𝐶𝐶𝑅𝑅𝑎𝑎 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝑅𝑅𝑎𝑎 �𝑠𝑠≥𝑛𝑛
Λ𝑠𝑠𝑛𝑛 Π𝑠𝑠𝑛𝑛 Γ𝑠𝑠−𝑎𝑎|𝑛𝑛−𝑎𝑎
Exposure
𝑅𝑅𝑎𝑎 = 1 + 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐴𝐴𝑎𝑎 �𝑋𝑋 − 𝑃𝑃𝑎𝑎 �𝑠𝑠≥𝑛𝑛
Λ𝑠𝑠𝑛𝑛 Π𝑠𝑠𝑎𝑎 Γ𝑠𝑠−𝑎𝑎|𝑛𝑛−𝑎𝑎
…
ΠΛ
na s t
Γ
ΠΛ
na s t
Γ
26
Reserves
past & future interests + procrastination
accidenttime
closurenotification now
future inflation
past interests + procrastination
accidenttime
nownotification closure
past inflation
as-is → as-if
current → ultimate
27
Reserves
past & future interests + procrastination
accidenttime
closurenotification now
future inflation
current → ultimate0
1'000'000
2'000'000
3'000'000
4'000'000
5'000'000
6'000'000
7'000'000
2'013 2'014 2'015 2'016 2'017 2'018 2'019 2'020 2'021
best estimate
future 1
future 2
29
Forecast the Future
30
Conclusions
Argentina is complex
ESG are important
AvE are important
Actuarial techniques are not science, they are engineering
31
Reserving
Different models depending on data availability / quality line of business / market processes / products … actuarial judgment
→ 1st moment of a distribution
standard reserving model
Solvency II
Different models depending on data availability / quality line of business / market processes / products … actuarial judgment
→ nth moment of a distribution
standard solvency formula
Different models depending on data availability / quality line of business / market processes / products … actuarial judgment
… et Carthago delenda est!
32
BOF
Standard Solvency II formula Analytic linear approximation
𝑆𝑆𝐶𝐶𝑅𝑅 ← 𝜎𝜎2 = ∑𝜌𝜌𝑖𝑖𝑖𝑖𝜎𝜎𝑖𝑖𝜎𝜎𝑖𝑖 Probe the tail with 2nd moments
Internal models Numerical aggregation of realistic distributions
𝑆𝑆𝐶𝐶𝑅𝑅 ← risk1 ⊗ risk2 ⊗ risk3 ⊗⋯ Probe the true tail
… et Carthago delenda est!
33
BOF
Internal model Numerical aggregation of realistic distributions
𝑆𝑆𝐶𝐶𝑅𝑅 ← risk1 ⊗ risk2 ⊗ risk3 ⊗⋯ Probe the true tail
… et Carthago delenda est!
Cut along dotted line
