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Review Exercises_2011

Course: ACTSC 463, Fall 2011
School: Waterloo
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XYZ 1. Insurance Company has been writing business since 1/1/2005 and has provided you with following incurred loss data evaluated at 12/31/2009: Report Year Accident Year 2005 2006 2007 2008 2009 10,000 4,000 2,000 1,000 2005 12,000 5,000 2,500 1,500 2006 16,000 6,500 3,500 2007 18,000 7,000 2008 20,000 2009 Development Interval 1-2 Years 2-3 Years 3-4 Years 4-5 Years 5-Ultimate Accident Year Report Year 1.50...

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XYZ 1. Insurance Company has been writing business since 1/1/2005 and has provided you with following incurred loss data evaluated at 12/31/2009: Report Year Accident Year 2005 2006 2007 2008 2009 10,000 4,000 2,000 1,000 2005 12,000 5,000 2,500 1,500 2006 16,000 6,500 3,500 2007 18,000 7,000 2008 20,000 2009 Development Interval 1-2 Years 2-3 Years 3-4 Years 4-5 Years 5-Ultimate Accident Year Report Year 1.50 1.10 1.25 1.10 1.10 1.00 1.10 1.00 1.05 1.00 Assuming the development factors are correct, estimate unreported losses as of 12/31/2009. 1. Solution Calculate 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 Year 1.500 1.250 1.100 1.100 1.050 Cumulative AY 2.382 1.588 1.271 1.155 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 RY Incurred to AY/RY to Date AY LDF AY Ultimate 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 RY LDF RY Ultimate 1.000 10,000 1.000 16,000 1.000 23,000 1.100 30,800 1.210 38,720 118,520 2. List two things that make the selection of a tail factor difficult. 2. Solution: i) Limited data ii) leveraging effect 3. What is the estimate of unpaid claims as of 12/31/2009 for accident years 2005 to 2009, using the Bornhuetter-Ferguson technique and the following information? Accident Year 2005 2006 2007 2008 2009 Expected Ult Claim Claims Paid to Earned Premium Ratio Date 1,000,000 650,000 0.65 1,000,000 650,000 0.65 1,000,000 500,000 0.70 1,000,000 500,000 0.70 1,000,000 500,000 0.80 Accident Year Ultimate Paid Development Factors 2009 to Ultimate 2.000 2008 to Ultimate 1.600 2007 to Ultimate 1.250 2006 to Ultimate 1.105 2005 to Ultimate 1.000 3. Solution Since loss development factors are for paid losses we can calculate unpaid losses directly: Expected Accident Ult Claim Year Earned Premium Ratio % Unpaid Unpaid 1,000,000 0.0% 2005 0.65 1,000,000 9.5% 61,765 2006 0.65 1,000,000 20.0% 140,000 2007 0.70 1,000,000 37.5% 262,500 2008 0.70 1,000,000 50.0% 400,000 2009 0.80 Total 5,000,000 864,265 4. You are given the following information as at December 31, 2009: Accident Year 2006 2007 2008 2009 Earned Premium Incurred Loss 15,000 16,000 17,000 18,000 4,500 4,800 3,200 2,500 Incurred LDF to Ultimate 1.500 1.750 2.000 4.500 The expected loss ratio for all accident years is 65%. The company has no exposure prior to 2006. a) Use the Bornhuetter-Ferguson method to calculate the IBNR for AY 2009 at December 31, 2009. b) Use the Cape Cod technique to calculate the IBNR for AY 2009 at December 31, 2009. c) Which method would you choose and why? 4. Solution a) Accident Year 2006 2007 2008 2009 Earned Premium Incurred Loss Incurred LDF to Ultimate 15,000 16,000 17,000 18,000 4,500 4,800 3,200 2,500 1.500 1.750 2.000 4.500 Earned Premium Incurred Loss Incurred LDF to Ultimate 15,000 16,000 17,000 18,000 4,500 4,800 3,200 2,500 1.500 1.750 2.000 4.500 Expected % Unreported Loss Ratio B-F Method 33.3% 65% 3,250 42.9% 65% 4,457 50.0% 65% 5,525 77.8% 65% 9,100 Solution b) Accident Year 2006 2007 2008 2009 Total 66,000 15,000 % Unreported 33.3% 42.9% 50.0% 77.8% % Reported 66.7% 57.1% 50.0% 22.2% Used Up Premium 10,000 9,143 8,500 4,000 31,643 Cape Cod LR 45.0% 52.5% 37.6% 62.5% 47.4% 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. Cape Cod IBNR 2,370 3,251 4,029 6,637 16,287 5. You are given the following information for a line of business: Disposal Rates Report Year 0-12 2006 0.50 2007 0.45 2008 0.55 2009 0.55 Report Year 2006 2007 2008 2009 Paid Severities 12-24 0.25 0.15 0.20 # of Reported Claims 120 140 160 200 24-36 0.15 0.24 Interval 0-12 12-24 24-36 37-Ult 37-Ult 0.10 0-12 800 840 900 950 12-24 24-36 1,200 1,300 1,500 37-Ult 1,600 1,800 2,000 Annual Paid Severity Trend 5% 10% 12% 15% Use the Adler-Kline technique to estimate ultimate claims for all report years. 5. Solution Select disposal Ratios. Report Year 0-12 2006 0.50 2007 0.45 2008 0.55 2009 0.55 Select 0.50 Calculate future claim closings 12-24 0.25 0.15 0.20 0.20 Calculated Trended Paid Severities Report Year 0-12 12-24 926 1,597 2006 926 1,573 2007 945 1,650 2008 950 2009 Select 937 1,607 Report Year 2006 2007 2008 2009 Total Ultimate RY Losses 136,800 191,300 222,413 298,198 848,712 24-36 0.15 0.24 0.20 37-Ult 0.10 Report Year 2006 2007 2008 2009 0-12 12-24 60 63 88 110 24-36 30 21 32 37-Ult 18 34 27 36 36 Ultimate 120 22 140 13 160 18 200 12 0.10 Actual Paid Severities 24-36 37-Ult 2,248 2,258 3,042 2,253 3,042 Report Year 2006 2007 2008 2009 Select 0-12 12-24 24-36 37-Ult 800 840 900 950 1,200 1,300 1,500 1,607 1,600 1,800 2,253 2,253 2,000 2,300 2,645 3,042 937 1,607 2,253 3,042 6. For each of the techniques listed below, explain how and why each would react to data with claim ratio deterioration and case outstanding strengthening: a) Incurred loss development technique b) Incurred Bornhuetter-Ferguson technique c) Expected loss ratio technique d) Paid development technique 6. Solution a) IBNR would be overstated. The incurred development technique reacts appropriately to loss 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. You are given the following information: AY 2007 2008 2009 AY 2007 2008 2009 Cumulative Paid Losses 12 24 29,040 38,100 32,000 41,900 70,400 36 65,800 Cumulative Closed Counts 12 24 40 50 40 50 80 AY 2007 2008 2009 36 70 Ultimate 90 130 140 AY 2007 2008 2009 Cumulative Incurred Losses 12 24 36 40,740 62,700 50,880 30 60 40 a) Using the Berquist-Sherman reserve adequacy method develop an adjusted case outstanding triangle. Assume the actual loss trend is 5% and start with the latest diagonal. b) Using the Berquist-Sherman closure rate method develop an adjusted paid loss triangle. Select disposal ratios from the latest diagonal and use linear interpolation to calculate the paid losses. c) Using your answers to a) and b), derive an adjusted cumulative incurred loss triangle. d) an Use incurred development method to calculate the adjusted IBNR for AY 2009. Assume a geometric average for selection of the 12-24 month development factor. a) Calculate case outstanding triangle. AY 12 24 11,700 20,000 2007 24,600 26,250 2008 18,880 2009 Calculate average case o/s triangle AY 12 24 390 500 2007 410 525 2008 472 2009 Trend average case backwards at 5% AY 12 24 428.12 500.00 2007 449.52 525.00 2008 472.00 2009 Calculate adjusted case triangle AY 12 24 12,844 20,000 2007 26,971 26,250 2008 18,880 2009 36 17,100 36 855 36 855.00 36 17,100 b) Calculate disposal ratios and select latest diagonal AY 12 24 36 44.44% 55.56% 77.78% 2007 38.46% 61.54% 2008 28.57% 2009 Select 28.57% 61.54% 77.78% Calculate adjusted paid losses by interpolation of factors AY 12 24 36 18,669 48,335 65,800 2007 28,303 70,400 2008 32,000 2009 c) Sum the adjusted case and adjusted paid triangles. AY 12 24 36 31,512 68,335 82,900 2007 55,274 96,650 2008 50,880 2009 d) Calculate development factors and use geometric average to select 36-Ult AY 12-24 24-36 2.169 1.213 2007 1.749 2008 Select 1.947 1.213 1.05 2.480 Cumulative 1.274 1.05 IBNR = (2.137-1)(50,880) 75,323.44 82,900 Open Claim Counts 12 24 The selected incurred development factor from 36 months to ultimate is 1.05. 7. Solution 61,900 96,650 40 50 36 20 8. You are given the following information: Calendar Year 2007 2008 2009 Paid ULAE 175,000 100,000 100,000 # Open Claims at Year End 105 100 110 Claims Opened During Year 10 20 75 ULAE is incured throughout the life of the claim The cost of claim file maintenance is twice as great in the first year as in subsequent years. Assume no inflation There is no need to adjust for claims closed during the year. Using the Wendy Johnson technique, what is the expense per open claim for calendar year 2009? 8. Solution Determine weighted number of open claims. =110+75 = 185 Expense per open claim is =100,000/185 540.54 9. You are given the following data for a line of business: Cumulative Incurred Losses Earned AY Premium 12 24 36 2006 1200 300 600 750 2007 1400 400 800 1000 2008 1500 500 1000 2009 2000 600 48 825 You have been informed that the company's actuary has correctly applied the Bornhuetter-Ferguson technique and estimated unpaid claims at $1,300. Assuming that claims are completely developed at 48 months, calculate the expected claim ratio underlying the estimate. Assume that all years have the same ratio. Show all work. 9. Solution Calculate LDFs and make selections: AY 12 24 2006 2.00 1.25 2007 2.00 1.25 2008 2.00 Select 2.00 1.25 Cumulative 2.75 1.375 36 1.10 1.10 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. You are given the following information about an insurance company's liabilities: Cumulative Paid Losses Accident Year 2006 2007 2008 2009 2010 12 24 6,338 6,075 7,290 8,201 7,715 36 8,809 9,113 7,594 10,024 - 48 9,094 9,799 8,123 - 60 9,300 9,900 9,300 Ultimate 0 0 0 0 0 0 0 9,300 9,900 8,646 11,078 10,706 The market rate of return on the assets supporting the liabilities is 5%. The company uses an asset-liability matching strategy to perfectly hedge interest rate movements. The long-term credit spread on the assets is 25 basis points. The claims development PFAD is 10% for all years. There is no reinsurance assumed or ceded. a) Calculate the interest rate PFAD based on the explicit quantification approach. b) Assuming an interest rate PFAD of 100 basis points and simple averaging for selection of a payment pattern, what is the Actuarial Present Value (discounted value) of the outstanding claim liabilities? 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 2006 2007 2008 2009 2010 Select Incremental Cumulative 0-12 36-48 48-60 68.1% 61.4% 84.3% 74.0% 72.1% 12-24 94.7% 92.0% 87.8% 90.5% 24-36 97.8% 99.0% 93.9% 100.0% 100.0% 100.0% 72.0% 72.0% 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 Ultimate 2014 9,300 9,900 8,646 11,078 10,706 Calculate discount factors Accident Year 2006 2007 2008 2009 2010 2010 2011 0.0% 0.0% 100.0% 64.5% 68.8% Discounted @ 5% Accident Year 2006 2007 2008 2009 2010 2012 0.0% 0.0% 0.0% 35.5% 20.1% 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% 0.5 1.5 2.5 3.5 4.5 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% Int PFAD 2 8 25 35 Claim PFAD % 10% 10% 10% 10% 10% Accident Year Outstanding Disc @ 5% 2007 523 511 2008 1,054 1,011 2009 2,991 2,861 2010 Total 4,568 4,382 Disc @ 4.0% 513 1,019 2,886 4,418 Discounted @ PFAD rate = 4% Accident Year Total 0.5 0.0% 0.0% 2005 0.0% 0.0% 2006 97.6% 98.1% 2007 95.9% 63.3% 2008 95.7% 67.5% 2009 Claim PFAD 51 101 286 438 Total PFAD - 54 109 311 474 APV - 564 1,120 3,172 4,856 4% 1.5 2.5 3.5 4.5 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% Total 0.0% 0.0% 98.1% 96.7% 96.5% 11. You are given the earned premiums and incurred losses for a small book of business as follows: Cumulative Incurred Losses ($000s) Age of Development Earned Premium 8,100 8,450 8,800 9,150 9,500 9,850 AY 2005 2006 2007 2008 2009 2010 12 100 1750 600 350 1230 300 24 420 2000 2700 830 1750 36 1320 1900 2700 4300 48 3400 4500 2850 60 7100 9500 You believe that the changes in the book of business are accurately reflected in the earned premiums. Using the least-squares development method, estimate the ultimate losses for accident year 2009. Assume a 60-to-ultimate loss development factor of 1.100 for all accident years. Show all work. 11. Solution (note: the ideal solution would use loss ratios instead of loss dollars, but the derivation is the same. 7,810 AY 2005 Ultimate = 7100 x 1.1 10,450 AY 2006 Ultimate = 9500 x 1.1 6,490 AY 2007 Ultimate = as below 5,457 AY 2008 Ultimate = as below AY 2009 Ultimate = as below AY 2010 Ultimate = as below 7,655 4,763 Start with AY 2007: Use data from AY 2005 and 2006 Average Y: 9130 36,789,500 Average XY: b: 2.4 AY 2007 Ultimate: 1973.3333 4214133 10618.986 Average X: Average X^2: a: 1487.5 3038825 6966.6863 Average X: Average X^2: a: 1540 3804450 4083.9363 7,655 AY 2010: Use data from AY 2005 - 2009 Average Y: 7,572 14,907,134 Average XY: b: 2.2652083087 AY 2010 Ultimate: Average X: Average X^2: a: 5,457 AY 2009: Use data from AY 2005 - 2008 Average Y: 7,552 11,558,094 Average XY: b: 0.3932927381 AY 2009 Ultimate: 3950 15905000 -350 6,490 AY 2008: Use data from AY 2005 - 2007 Average Y: 8250 15,895,733 Average XY: b: -1.2004998611 AY 2008 Ultimate: Average X: Average X^2: a: 4,763
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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
GWU - CSC - 6232
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 -
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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:
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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
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Concurrency, 3C03, 2002Answer Question 1 and two further questions.Marks for each part of each question are indicated in square brackets1.rsCalculators are NOT permitteda. Show an equivalent labelled transition system for each of the following FSP p