Claims Provisions

FSAP
Actuarial Valuation of
General Insurance Claims Provisions

Instituto de Seguros de Portugal
01/02/2006


Claims Provisions
Summary
1. Underlying principles
2. Information reported by insurance undertakings
3. Supervisory process
3.1. Ratio Analysis
3.2. Statistical Approaches
4. Responsible actuaries practice


Claims Provisions
1. Underlying principles
• Adequate claims provisions are essential for the financial
soundness of general insurance companies
• Claims provisions should correspond to a reasonably
conservative estimate of the amount of future payments
arising from claims incurred before the valuation date:
Claims Reported to the insurance company
Claims Incurred but Not Reported (IBNR)
Claims Management Costs
• Statistical methods are commonly used for the estimation
of claims provisions

Claims Provisions
2. Information reported by insurance undertakings
• ISP supervisory analysis is based on:
 Responsible Actuary’s report
 Auditor’s appraisal
 Run-off triangles (claims paid, claims provision, number of
claims) for main LOB’s:
 Motor (also by coverage)
 Property claims
 Liability claims
 Workers’ compensation
 Temporary incapacity
 Long-term assistance
 Health
 Individual insurance
 Group insurance
 Other relevant statistical data (e.g. premiums, number of
policies, Claims settlement expenses, etc.)

• Data quality is crucial


Claims Provisions
3. ISP Supervisory Process
• ISP pays particular attention to the responsible actuary’s
critical analysis of the claims provision estimates
• Several ratios are computed and analysed
• ISP runs various statistical methods (deterministic and
stochastic) to estimate the expected value and variability

of the claims provision
• A detailed technical and practical manual is available to
ISP supervision staff as a guidance for the analysis of
claims provisioning (off-site and on-site analysis)


Claims Provisions
3.1. Ratio Analysis
•

Ratios and indicators considered on ISP analysis of claims
provisions:
 Growth on Premiums
 Average Premium
 Loss Ratio
 Average Cost of New Claims
 Average Claims Provision
 Claims Frequency
 Development of Claims Payments
 “Speed” of Process closure
 Re-openings
 Claims Expenses
 Provisioning, including IBNR
 Readjustments

•

Ratios are calculated individually and compared on a static and
evolutionary perspective with peer group and market benchmarks

Claims Provisions
3.2. Statistical Approaches
• The statistical methods’ objective is to project the
expected future claims experience, using assumptions
based on past data analysis complemented with expert
opinion
• The analysis should consist of:
 Analysis of results (particularly the estimation error),
taking into account the theoretical assumptions
underlying each model
 Analysis of relevant graphs and hypothesis tests to assess
each models’ fitness


Claims Provisions
3.2. Statistical Approaches (cont.)
• Format of a Run-off triangle representing accident year x development
year
• Run-off triangles may refer to:
 Number of claims
 Claims paid (common approach)
 Claims incurred, i.e. Claims paid + Claims provision

Accident year

• Aim is to estimate the lower unknown
triangle (shaded):
Development year
1997

1998
1999
2000
2001
2002
2003
2004
2005

0
45.591
48.639
50.007
53.871
55.158
49.106
51.372
53.832
50.825

1
17.534
20.062
28.797
30.759
29.658
30.203
28.112
27.492

2
5.430
5.460
7.722
7.750
8.802
7.369
7.501

3
4.700
3.988
6.474
5.121
5.297
7.250

4
3.486
3.655
5.269
4.205
5.189

5
2.821
4.556
4.859
5.725

6
3.590
2.390
4.074

7
2.728
2.740

8
2.003

>8
1.358

(m.u.: thousand euros)


Claims Provisions
3.2. Statistical Approaches (cont.)
• Deterministic methods
 Projection of past claims experience assuming fixed
development factors
 Provides point estimates of the expected future claims amounts
 Various actuarial techniques are available
• Stochastic models
 Random nature of variables is considered
 Generally speaking, the future claims amounts are assumed to
follow a specified probability distribution
 Allows for the measurement of the estimates variability,

essential for the construction of confidence intervals for the
estimates
 Various actuarial models are available


Claims Provisions
3.2. Statistical Approaches (cont.)
Statistical Methods available at ISP
• ISP has in-house built programs that allow for the automatic
testing of the following statistical methods:
Deterministic

Stochastic

Grossing Up

Thomas Mack Model

Link Ratio

Generalised Linear Models:

Chain-Ladder

Over-dispersed Poisson

Taylor

Gamma

Loss Ratio

Inverse Gaussian

Bornhuetter-Ferguson

Loglinear Model (Kremer)

Stress Testing
Bootstrap simulation
(VaR and
Tail VaR
calculations)

• Some of the methods consider:
 Possibility for inflation correction
 Variant approaches based on different assumptions
 Advanced refinements to include reparameterization and
expert opinion


Claims Provisions
3.2. Statistical Approaches (cont.)
Statistical Approaches – Example
• Results from running the programs for the previous run-off triangle:
Provision
held

Best
Estim ate

Estim .
Error

Estim .
Error (%)

BE
BE
Sufficiency
Sufficiency
(%)

Suffic.
Probab.
Norm al

Suffic.
Probab.
Lognorm al

DETERMINISTIC
Grossing Up - Average

198.594

183.294

15.300

8%

Link Ratio - Average

198.594

183.760

14.834

8%

Grossing Up - Weighted

198.594

183.294

15.300

8%

Link Ratio - Weighted

198.594

183.760

14.834

8%

Chain Ladder - no inflation

198.594

184.319

14.275

8%

Chain Ladder - w / inflation

198.594

184.624

13.970

8%

Mack's Model

198.594

184.319

8.644

5%

14.275

8%

95%

95%

ODP

198.594

184.319

13.121

7%

14.275

8%

86%

86%

ODP - Bootstrap

198.594

184.319

13.751

7%

14.275

8%

85%

85%

Gamma

198.594

188.328

12.367

7%

10.266

5%

80%

80%

Gamma - Bootstrap

198.594

188.328

12.415

7%

10.266

5%

80%

80%

Inv. Gauss.

198.594

189.225

28.180

15%

9.368

5%

63%

66%

Inv. Gauss. - Bootstrap

198.594

189.225

28.699

15%

9.368

5%

63%

65%

Loglinear

198.594

191.399

12.850

7%

7.195

4%

71%

72%

Loglinear - Bootstrap

198.594

191.399

12.917

7%

7.195

4%

71%

72%

STOCHASTIC

m.u.: thousand euros


232.013

229.151

226.290

223.429

220.568

217.707

214.846

211.985

209.124

206.263

203.402

200.541

197.679

194.818

191.957

189.096

186.235

183.374

180.513

177.652

174.791

171.930

169.069

166.207

163.346

160.485

157.624

154.763

151.902

149.041

146.180

143.319

140.458

137.597

Claims Provisions

3.2. Statistical Approaches (cont.)

Statistical Approaches – Example (cont.)
• Simulated empirical distribution of the total claims provision using
Bootstrap ODP stochastic model:
350

300

250

200

150

100

50

0


Claims Provisions
3.2. Statistical Approaches (cont.)
Statistical Approaches – Example (cont.)
• Goodness-of-fit tests for the Analytic ODP stochastic model:
Test: Significance of model
Parâm.
Estim.
M
10,62361766
A1998
0,063261536
A1999
0,253050203
A2000
0,291874246
A2001
0,309298151
A2002
0,254721372

A2003
0,241283213
A2004
0,262774653
A2005
0,212529774
B1
-0,65074148
B2
-1,956979381
B3
-2,218541598
B4
-2,434593748
B5
-2,373562924
B6
-2,617893165
B7
-2,74215242
B8
-3,021378097
B9
-3,410210981

parameters
EP
0,048932988
0,063706426
0,061666529

0,061832402
0,062455212
0,064085587
0,065434972
0,066738007
0,077018058
0,03587058
0,063860539
0,077551497
0,09410069
0,10359585
0,137099385
0,184910402
0,303590867
0,367195751

%
0,46%
100,70%
24,37%
21,18%
20,19%
25,16%
27,12%
25,40%
36,24%
5,51%
3,26%
3,50%
3,87%

4,36%
5,24%
6,74%
10,05%
10,77%

W
47134,76939
0,98608188
16,83892524
22,28226398
24,52546637
15,79828854
13,59672679
15,50316883
7,614728641
329,1093138
939,09028
818,3795636
669,3717645
524,9486045
364,6135692
219,9178577
99,04504351
86,25160822
Nív. Sig.:

X^2(1)
3,841455338
3,841455338

3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
3,841455338
5,00%

Decisão
Par. Não Nulo
Par. Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo

Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo
Par. Não Nulo

P-value
0,00%
32,07%
0,00%
0,00%
0,00%
0,01%
0,02%
0,01%
0,58%
0,00%
0,00%
0,00%
0,00%
0,00%
0,00%
0,00%
0,00%
0,00%


Claims Provisions

3.2. Statistical Approaches (cont.)
Statistical Approaches – Example (cont.)
3

Test: Assumption of normality of residuals
y = 1,038x - 0,007
R2 = 0,9774
2

1

0
-2,5

-2,0

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

2,0

2,5

-1

-2

-3
3,0000

Test: Trends on residuals per development year

2,0000

1,0000

0,0000
0

-1,0000

-2,0000

-3,0000

1

2

3

4

5

6

7

8

>


Claims Provisions
4. Responsible actuaries practice
•

The company’s responsible actuary is expected to perform
regular valuations of technical provisions (including claims
provisions), using whatever methods he considers to be more
reasonable

•

The analysis performed by responsible actuaries involves, in
most cases, the use of deterministic methods and, increasingly,
the use of stochastic methods

•

ISP recommendations:
•
•
•
•

Enhancement of the quality of the information
Estimation of the provision for management costs
Encouragement for the use of stochastic models
Highlight on the importance of testing the assumptions
underlying each particular model – there is not an optimal
model adjusted for all situations


Claims Provisions
Risk oriented approach
The supervisory process of claims provisions
analysis provides one important input for the
global risk oriented framework