Technical Reserves: A Practical
Role for Actuaries
Ghazi Naceur
King Saud University
08 February 2017
Plan
I.
General Concept
II.
Technical Reserving for a (Re)insurance Company
III. Case Study
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General Concept
3
1.
What is Reserving ?
2.
Claims reserves
3.
Premium reserves
4.
Statistical Data
5.
Case Study , Motor LOB
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1. What is reserving ?
 The inversion of cycle of production is characteristic of the insurance industry, in fact the
(Re)insurance companies receives the premium before paying the claims (losses).
 The aim of the insurance activity is to pay large amounts of losses to the insured, it usually happen
that the premiums collected are not enough to cover the future claims cost.
 In this context insurance/reinsurance companies has to keep a certain amount of the received
premium untouched and reserve it for future payments of incurred claims.
 There is two types of reserves :
– Claims reserves
– Premium reserves
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2. Claims Reserves
2.1 Definition
The claims reserves are the amount of future payments (including expenses) related to claims that have
occurred up to the valuation date.
2.2 Components of claim reserves
 Outstanding claims amount that is known/reported.
 Incurred But Not Reported (IBYNR) - losses that have occurred but not yet known/reported.
 Incurred But Not Enough Reported (IBNER) - further development on known claims due inadequate
case reserves or claims deterioration.
 IBNYR and IBNER are usually combined under the name of IBNR and are estimated by Actuaries.
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3. Premium Reserves
3.1 Definition
The premium reserves are the amount premium that should be allocated to the unexpired period of
time up to valuation date ( accounting closing date) .
3.2 Components of premium reserves
 Unearned premium reserves (UPR) - premiums that are set aside due to the corresponding period of
contract cover has not yet lapsed.
 Premium Deficiency Reserves (PDR) - is the reserve required to recognize the inadequacy of pricing
and underestimation of the losses amount up to a valuation date.
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4. Statistical data ( information)
4.1 Why do we need statistics and data?
 Determine expected loss ratio and claims distribution.
 Analyze claims development pattern /trends over the time.
 Combine homogenous data that provides size and credibility for Actuarial analysis.
4.2 Types of information and statistical data
 Historical losses and premium data – for long term , data will organized in triangles.
 Current data - budget, business plan, profitability analysis.
 Data about future - EPI, pipelines, late notifications, claims management.
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4. Statistical data (Type & Mix)
Possible breakdown structure of the data
 Line of business
 Underwriting Year
 Facultative VS treaty for reinsurance companies
 Geographical regions (e.g. countries)
 Attritional loss vs Large/CAT loss
 Structure depends on data credibility and portfolio mix
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4. Statistical data (Methods)
 You are about to make a journey on the train
that lasts 10 stations
 Before you depart you are told that it will take
2 minutes to travel between stations
 You set off…
 …. And after 10 minutes you’ve only gone 2
stations
Possible Solutions :
 Ignore any development
 Ignore any prior knowledge & assume the new trend will continue
 Use actual development and prior knowledge of the
future
 How long do you think your whole journey will
take?
-> Bornhuetter Ferguson estimates of 26 minutes
=
10
+
8x2
=
Actual to date +
Expected Future
=
(50 x 2/10)
+
(20 x 8/10)
= DFM x %Developed + Prior x (1 - % Developed)
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5. Case Study : Motor LOB
 A simple reserving exercise for Motor Class.
 Reserving exercise performed as at financial year end.
 Actual data used.
 No breakdown; combination of treaty and facultative for all regions.
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Case Study : Motor LOB
 Gross Premiums
Underwriting
Year
2009
2010
2011
2012
2013
2014
Total
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Gross Premium
3,839,883
8,666,018
8,126,972
15,907,659
53,158,830
19,954,250
109,653,612
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Case Study : Motor LOB
 Claims triangle
Claims Incurred Triangle (Att)
Underwriting
Year
2009
2010
2011
2012
2013
2014
Total
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1yr
488,621
2,139,761
1,398,611
1,919,547
3,733,401
2,737,867
12,417,808
2yr
2,004,880
5,470,629
4,449,397
4,938,857
28,006,950
3yr
2,513,684
6,342,391
5,332,194
7,725,431
4yr
2,650,146
6,444,862
6,055,171
5yr
2,665,847
6,884,371
6yr
2,760,850
44,870,714
21,913,700
15,150,179
9,550,218
2,760,850
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Case Study : Motor LOB
 Claims triangle
Claims Incurred Triangle (large/cat)
Underwriting
Year
2009
2010
2011
2012
2013
2014
Total
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1yr
0
0
3,126,816
0
0
0
3,126,816
2yr
3yr
4yr
5yr
6yr
403,395
3,324,578
3,294,690
0
0
372,043
1,855,843
3,342,988
102,500
349,598
1,869,236
3,175,268
349,417
1,868,299
349,417
7,022,663
5,673,374
5,394,102
2,217,715
349,417
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Case Study : Motor LOB
 Chain ladder Method
Development Factor
No split
Origin Period
(1) 12-24
2009
4.92872
2010
4.11037
2011
1.71124
2012
2.57293
2013
7.50173
2014
Selected LDF
2.63259
Cumulative DF
3.39174
%Reported (1/CDF)
29%
(2) 24-36
1.19825
0.93213
1.12023
1.58497
Attritional
(3) 36-48 (4) 48-60 (5) 60-72 (6) 72-Ult (1) 12-24
1.03951 1.00517 1.03151
4.10314
1.01413 1.05275
2.55665
1.06401
3.18130
2.57293
7.50173
1.15493 1.03974 1.04014 1.03151
1.28837 1.11554 1.07291 1.03151
78%
90%
93%
97%
(2) 24-36
1.25378
1.15935
1.19841
1.56421
(3) 36-48 (4) 48-60 (5) 60-72 (6) 72-Ult
1.05429 1.00592 1.03564
1.01616 1.06820
= 6,884,371 /
1.13559
1.00000 2.83590 1.29945 1.06780 1.05005 1.03564
1.00000 4.27915 1.50892 1.16120 1.08747 1.03564
100%
23%
66%
86%
92%
97%
6,444,862
1.00000
1.00000
100%
For each UWY, development factor from time t-1 to t = claim incurred at time t / claim incurred at time
t-1
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Case Study : Motor LOB
 Chain ladder Method
% Reported – No split
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% Reported – Attritional
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Case Study : Motor LOB
 Ultimate Claims Selection
Attritional
Underwriting
Year
2009
2010
2011
2012
2013
2014
Total
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Expected
Chainladde
Selected
Ultimate
Weight ELR r Ultimate Weight CL BF Ultimate Weight BF Ultimate
Claims
%
Claims
%
Claims
%
Claims
2,879,912
0% 2,760,850
100% 2,760,850
0% 2,760,850
6,499,514
0% 7,129,709
100% 7,108,023
0% 7,129,709
6,095,229
0% 6,584,824
100% 6,545,443
0% 6,584,824
11,930,744
0% 8,970,752
100% 9,381,659
0% 8,970,752
37,211,181
0% 42,260,355
0% 40,557,389
100% 40,557,389
13,967,975
100% 11,715,746
0% 13,441,649
0% 13,967,975
78,584,555
79,422,235
79,795,013
79,971,499
Large/cat
Total
Weight
100%
100%
100%
100%
100%
100%
Expected
Ultimate
Claims
349,417
1,868,299
3,175,268
102,500
1,063,177
598,628
7,157,287
Total
Selected
Ultimate
Claims
3,110,266
8,998,007
9,760,092
9,073,252
41,620,566
14,566,603
87,128,787
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Case Study : Motor LOB
 Results Year End
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Any Questions
Thank you