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8 Pages
Assignment 3 Solutions
Course: ACTSC 463, Fall 2011School: Waterloo
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Solution Calculate 1. ultimate AY and RY loss development factors: Cumulative LDFs Development Interval 1-2 Years 2-3 Years 3-4 Years 4-5 Years 5-Ultimate Accident Cumulative Year AY 1.500 2.382 1.250 1.588 1.100 1.271 1.100 1.155 1.050 1.050 Report Year 1.100 1.100 1.000 1.000 1.000 Cumulative RY 1.210 1.100 1.000 1.000 1.000 Calculate ultimate Accident Year and Report Year losses. AY Incurred to AY RY...
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Solution
Calculate 1. ultimate AY and RY loss development factors:
Cumulative LDFs
Development
Interval
1-2 Years
2-3 Years
3-4 Years
4-5 Years
5-Ultimate
Accident Cumulative
Year
AY
1.500
2.382
1.250
1.588
1.100
1.271
1.100
1.155
1.050
1.050
Report
Year
1.100
1.100
1.000
1.000
1.000
Cumulative
RY
1.210
1.100
1.000
1.000
1.000
Calculate ultimate Accident Year and Report Year losses.
AY
Incurred to
AY
RY Incurred
AY/RY
Date
AY LDF
Ultimate
to Date
2005
17,000
1.050
17,850
10,000
2006
21,000
1.155
24,255
16,000
2007
26,000
1.271
33,046
23,000
2008
25,000
1.588
39,700
28,000
2009
20,000
2.382
47,640
32,000
Total
109,000
162,491
109,000
Estimated unreported losses = AY Ultimate - RY Ultimate
43,971
2. Solution:
i) Limited data
ii) leveraging effect
RY LDF
1.000
1.000
1.000
1.100
1.210
RY
Ultimate
10,000
16,000
23,000
30,800
38,720
118,520
3. Solution
Since loss development factors are for paid losses we can calculate unpaid losses directly:
Expected
Accident
Earned
Ult Claim
Year
Premium
Ratio
% Unpaid
Unpaid
2005
1,000,000
0.65
0.0%
2006
1,000,000
0.65
9.5%
61,765
2007
1,000,000
0.70
20.0%
140,000
2008
1,000,000
0.70
37.5%
262,500
2009
1,000,000
0.80
50.0%
400,000
Total
5,000,000
864,265
4. Solution a)
Incurred
Expected
Accident Earned
Incurred LDF to
%
Loss
Year
Premium
Loss
Ultimate Unreported Ratio
2006
15,000
4,500
1.500
33.3%
65%
2007
16,000
4,800
1.750
42.9%
65%
2008
17,000
3,200
2.000
50.0%
65%
2009
18,000
2,500
4.500
77.8%
65%
B-F
Method
3,250
4,457
5,525
9,100
Solution b)
Incurred
Accident Earned
Incurred LDF to
%
%
Used Up Cape Cod Cape Cod
Year
Premium
Loss
Ultimate Unreported Reported Premium
LR
IBNR
2006
15,000
4,500
1.500
33.3%
66.7%
10,000
45.0%
2,370
2007
16,000
4,800
1.750
42.9%
57.1%
9,143
52.5%
3,251
2008
17,000
3,200
2.000
50.0%
50.0%
8,500
37.6%
4,029
2009
18,000
2,500
4.500
77.8%
22.2%
4,000
62.5%
6,637
Total
66,000
15,000
31,643
47.4%
16,287
Solution c)
Depends on how much information you have about the expected loss ratio of 65%. The Cape Cod uses
actual experience to select the loss ratio so is more appropriate in some situations.
5. Solution
Select disposal Ratios.
Report
Year
0-12
2006
0.50
2007
0.45
2008
0.55
2009
0.55
Select
0.50
12-24
0.25
0.15
0.20
24-36
0.15
0.24
37-Ult
0.10
0.20
0.20
Calculate future claim closings
Report
Year
0-12
12-24
2006
60
30
2007
63
21
2008
88
32
2009
110
36
0.10
Calculated Trended Paid Severities
Report
Year
0-12
12-24
24-36
2006
926
1,597
2,248
2007
926
1,573
2,258
2008
945
1,650
2009
950
Select
937
1,607
2,253
37-Ult
3,042
3,042
Actual Paid Severities
Report
Year
0-12
12-24
2006
800
1,200
2007
840
1,300
2008
900
1,500
2009
950
1,607
Select
937
1,607
24-36
18
34
27
36
24-36
1,600
1,800
2,253
2,253
2,253
37-Ult Ultimate
12
120
22
140
13
160
18
200
37-Ult
2,000
2,300
2,645
3,042
3,042
Report Ultimate RY
Year Losses
2006
136,800
2007
191,300
2008
222,413
2009
298,198
Total
848,712
6. Solution
a) IBNR would be overstated. The incurred development technique reacts appropriately to
l oss ratio deterioration, but will overstate when there is case strengthening.
b) The B-F method understates when there is loss ratio deterioration and overstates when
there is case reserve strengthening.
c) The expected loss technique will appropriately reflect case reserve strengthening, but
doesn't reflect loss ratio deterioration so will understate unless you adjust the LR.
d) Paid development is independent of case reserves so is unaffected by strengthening.
It also reflects loss ratio deterioration appropriately.
7. Solution
a)
Calculate case outstanding triangle.
AY
12
24
2007
11,700
20,000
2008
24,600
26,250
2009
18,880
Calculate average case o/s triangle
AY
12
24
2007
390
500
2008
410
525
2009
472
Trend average case backwards at 5%
AY
12
24
2007
428.12
500.00
2008
449.52
525.00
2009
472.00
Calculate case adjusted triangle
AY
12
24
2007
12,844
20,000
2008
26,971
26,250
2009
18,880
36
17,100
36
855
36
855.00
36
17,100
b)
Calculate disposal ratios and select latest diagonal
AY
12
24
36
2007
44.44%
55.56%
77.78%
2008
38.46%
61.54%
2009
28.57%
Select
28.57%
61.54%
77.78%
Calculate adjusted paid losses by interpolation of factors
AY
12
24
36
2007
18,669
48,335
65,800
2008
28,303
70,400
2009
32,000
c)
Sum the adjusted case and adjusted paid triangles.
AY
12
24
36
2007
31,512
68,335
82,900
2008
55,274
96,650
2009
50,880
d)
Calculate development factors and use geometric average to select
AY
12-24
24-36
36-Ult
2007
2.169
1.213
2008
1.749
Select
1.947
1.213
1.05
Cumulative
2.480
1.274
1.05
IBNR = (2.137-1)(50,880)
75,323.44
8. Solution
Determine weighted number of open claims.
=110+75 = 185
Expense per open claim is
=100,000/185
540.54
9. Solution
Calculate LDFs and make selections:
AY
12
24
36
2006
2.00
1.25
1.10
2007
2.00
1.25
2008
2.00
Select
2.00
1.25
1.10
Cumulative
2.75
1.375
1.1
Use B-F formula to calculate the ratio
Expected Unreported = Loss Ratio((1-1/1.1)(1400)+(1-1/1.375)(1500)+(1-1/2.75)(2000))
1300=Loss Ratio(1809.09)
Loss Ratio = 71.9%
10. Solution
a)
Sum of the credit spread, timing risk and mismatch risk
=25bp + .1(5%) + 0
0.75
=75 basis points
b)
Calculate payment pattern
Accident
Year
0-12
12-24
68.1%
61.4%
84.3%
74.0%
72.1%
72.0%
72.0%
100.0%
2006
2007
2008
2009
2010
Select
Incremental
Cumulative
36-48
48-60
94.7%
92.0%
87.8%
90.5%
24-36
97.8%
99.0%
93.9%
100.0%
100.0%
100.0%
91.3%
19.3%
28.0%
96.9%
5.6%
8.7%
100.0%
3.1%
3.1%
100.0%
0.0%
0.0%
2013
2014
Ultimate
9,300
9,900
8,646
11,078
10,706
Calculate discount factors
Accident
Year
2010
2011
0.0%
0.0%
100.0%
64.5%
68.8%
2006
2007
2008
2009
2010
Discounted @ 5%
Accident
Year
2006
2007
2008
2009
2010
Accident
Year
2007
2008
2009
2010
Total
0.0%
0.0%
0.0%
35.5%
20.1%
2012
0.0%
0.0%
0.0%
0.0%
11.1%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
5%
Discounted @ PFAD rate = 4%
0.5
1.5
2.5
3.5
4.5
Accident
Year
0.0%
0.0%
97.6%
63.0%
67.2%
0.0%
0.0%
0.0%
33.0%
18.7%
0.0%
0.0%
0.0%
0.0%
9.8%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
Outstandin
g
523
1,054
2,991
4,568
Disc @
5%
511
1,011
2,861
4,382
Disc @
4.0%
513
1,019
2,886
4,418
Claim
Int PFAD PFAD %
2
8
25
35
10%
10%
10%
10%
10%
Total
0.0%
0.0%
97.6%
95.9%
95.7%
Claim
PFAD
51
101
286
438
2005
2006
2007
2008
2009
Total
PFAD
54
109
311
474
4%
0.5
1.5
2.5
3.5
4.5
0.0%
0.0%
98.1%
63.3%
67.5%
0.0%
0.0%
0.0%
33.5%
19.0%
0.0%
0.0%
0.0%
0.0%
10.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
APV
564
1,120
3,172
4,856
Total
0.0%
0.0%
98.1%
96.7%
96.5%
11. Solution (note: the ideal solution would use loss ratios instead of loss dollars, but the derivation is the same.
AY 2005 Ultimate = 7100 x 1.1
7,810
AY 2006 Ultimate = 9500 x 1.1
10,450
AY 2007 Ultimate = as below
6,490
AY 2008 Ultimate = as below
5,457
AY 2009 Ultimate = as below
7,655
AY 2010 Ultimate = as below
4,763
Start with AY 2007:
Use data from AY 2005 and 2006
Average Y:
9130
Average XY:
36,789,500
b:
2.4
AY 2007 Ultimate:
1973.333
4214133
10618.99
Average X:
Average X^2:
a:
1487.5
3038825
6966.686
Average X:
Average X^2:
a:
1540
3804450
4083.936
7,655
AY 2010:
Use data from AY 2005 - 2009
Average Y:
7,572
Average XY:
14,907,134
b:
2.265208309
AY 2010 Ultimate:
Average X:
Average X^2:
a:
5,457
AY 2009:
Use data from AY 2005 - 2008
Average Y:
7,552
Average XY:
11,558,094
b:
0.393292738
AY 2009 Ultimate:
3950
15905000
-350
6,490
AY 2008:
Use data from AY 2005 - 2007
Average Y:
8250
Average XY:
15,895,733
b:
-1.200499861
AY 2008 Ultimate:
Average X:
Average X^2:
a:
4,763
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ConcurrencyState Models and Java ProgramsJeff MageeConcurrency: introductionandJeff Kramer1Magee/Kramer 2nd EditionWhat is a Concurrent Program?A sequential program has asingle thread of control.A concurrent program hasmultiple threads of cont
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Chapter 2Processes & ThreadsConcurrency: processes & threads1Magee/Kramer 2nd Editionconcurrent processesWe structure complex systems assets of simpler activities, eachrepresented as a sequential process.Processes can overlap or beconcurrent, so
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Chapter 3Concurrent ExecutionConcurrency: concurrent execution1Magee/Kramer 2nd EditionConcurrent executionConcepts: processes - concurrent executionand interleaving.process interaction.Models: parallel composition of asynchronous processes- int
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Chapter 4Shared Objects &Mutual ExclusionConcurrency: shared objects & mutual exclusion1Magee/Kramer 2nd EditionShared Objects & Mutual ExclusionConcepts: process interference.mutual exclusion.Models: model checking for interferencemodeling mutu
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Chapter 5Monitors &Condition SynchronizationConcurrency: monitors & condition synchronization1Magee/Kramer 2nd Editionmonitors & condition synchronizationConcepts: monitors:encapsulated data + access proceduresmutual exclusion + condition synchro
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Chapter 6DeadlockConcurrency: Deadlock1Magee/Kramer 2nd EditionDeadlockConcepts:system deadlock: no further progressfour necessary & sufficient conditionsModels:deadlock - no eligible actionsPractice:blocked threadsAim: deadlock avoidance - t
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Chapter 7Safety & LivenessPropertiesConcurrency: safety & liveness properties1Magee/Kramer 2nd Editionsafety & liveness propertiesConcepts:properties: true for every possible executionsafety: nothing bad happensliveness: something good eventuall
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Chapter 8Model-Based DesignConcurrency: model-based design1Magee/Kramer 2nd EditionDesignConcepts: design process:requirements to models to implementationsModels: check properties of interest:- safety on the appropriate (sub)system- progress on
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Chapter 9Dynamic SystemsConcurrency: dynamic systems1Magee/Kramer 2nd EditionDynamic SystemsConcepts: dynamic creation and deletion of processesResource allocation example varyingnumber of users and resources.master-slave interactionModels:stat
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Chapter 10Message PassingConcurrency: message passing1Magee/Kramer 2nd EditionMessage PassingConcepts: synchronous message passing - channelasynchronous message passing - port- send and receive / selective receiverendezvous bidirectional comms -
GWU - CSCI - 6907
CSci 6907: Data Managementand Exploration on the WebNan ZhangCourse InformationMeeting time: Mondays 06:10-08:40PM Meeting location: Philips Hall, Room 108Office Hours: Mondays 12:00-2:00pm Office: Academic Center 715 Phone: (202) 994-5919 Email:
GWU - CSCI - 6907
Preliminaries:Information RetrievalIntroductionText mining refers to data mining using text documents asdata. Most text mining tasks use Information Retrieval (IR)methods to pre-process text documents. These methods are quite different from traditi
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Information IntegrationAdapted from slides for Liu, Web Data Mining: Exploring Hyperlinks, Contents, and Usage Data, 2nd ed., Springer, 2009.Introduction Atthe end of last topic, we identified the problem ofintegrating extracted data:o column match
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WEB CRAWLINGOutline Motivation and taxonomy of crawlers Basic crawlers and implementation issues Universal crawlers Preferential (focused and topical) crawlers Crawler ethics and conflictsQ: How does asearch engineknow that allthese pagescontai
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DATA EXPLORATION AND PRIVACYPRESERVATION OVER HIDDEN WEBDATABASESNan Zhang, The George Washington University1*Collaborative work with Xin Jin of George Washington University,Arjun Dasgupta, Bradley Jewell, Anirban Maiti, and Dr. Gautam Dasof Univer