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{"sheet":"Problem","index":0,"n_rows":22,"n_cols":6,"rows_kept":22,"cut":false,"hidden":false,"merged":[[7,1,7,5],[15,0,15,4],[16,0,17,4],[18,0,18,1],[20,0,21,2],[19,0,19,5],[0,0,0,5],[1,0,1,5],[2,0,2,5],[3,0,3,5],[4,0,4,5],[6,0,6,5]]}
["Free Practice Problems for Casualty Actuarial Society Exam 7"]
["G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE"]
["http://rationalargumentator.com/actuaryguide/7-study-guide.html"]
["Inexhaustible Exam-Style Practice"]
["Based on Problem 9(a) - Spring 2011 CAS Exam 7"]
[]
["You are given the following triangle of cumulative paid-loss data:"]
[null,"Age of Development in Months"]
["Accident Year",12,24,36,48,60]
[2042,{"$f":"12300*D22","v":9722.9042172431946},{"$f":"B10+2500*(1-D22)","v":10246.704173088074},{"$f":"C10+1300*D22","v":11274.328196048737},{"$f":"D10+800*(1-D22)","v":11441.944181919098},{"$f":"E10+1200*D22*(1-D22)","v":11640.689813125966}]
[2043,{"$f":"19000*(1-D22)","v":3980.8796644210815},{"$f":"B11+5000*D22^2","v":7105.1729560360427},{"$f":"C11+3000*D22*(1-D22)","v":7602.0370340532108},{"$f":"D11+1900*D22","v":9103.9490676111018}]
[2044,{"$f":"B11*(1.7-1.1*D22)","v":3306.0090193295664},{"$f":"B12+0.5*C10","v":8429.3611058736024},{"$f":"C12+1100*D22","v":9298.8891253018555}]
[2045,{"$f":"10000+200*D22","v":10158.09600353241},{"$f":"B13*(1+D22)","v":18187.867911817491}]
[2046,{"$f":"(SUM(B10:B13)+12000)/5","v":7833.5777809052497}]
[]
["For an over-dispersed negative binomial model, the disperson parameter φ is",null,null,null,null,{"$f":"3*(D22+0.34)","v":3.3914400529861455}]
["Use the negative binomial model to calculate the mean and variance of the incremental claim amount for the following accident year:"]
[null,null,null,null,null,{"$f":"IF(D22<0.4,A10, IF(D22<0.7, A11, IF(D22<0.9,A12, A13)))","v":2044}]
["The incremental amount is from",null,{"$f":"IF(D22<0.1, 12, IF(D22<0.2,24, IF(D22<0.3, 36, IF(D22<0.4, 48, IF(D22<0.5, 12, IF(D22<0.6, 24, IF(D22<0.7, 36, IF(D22<0.8, 12, IF(D22<0.9, 24, 12)))))))))","v":12},"months to",{"$f":"C19+12","v":24},"months."]
["NOTE: Use volume-weighted chain-ladder loss-development factors to solve this problem."]
["TO RE-RANDOMIZE THE VALUES FOR THIS PROBLEM, CLICK ON THE FORMULA IN THE RED BOX AND PRESS \"ENTER\". That is all you need to do. "]
[null,null,null,{"$f":"StaticRand()","v":0.79048001766204834}]

{"sheet":"Solution","index":1,"n_rows":13,"n_cols":7,"rows_kept":13,"cut":false,"hidden":false,"merged":[[9,0,9,2],[11,1,11,2],[10,1,10,2],[12,1,12,2],[0,0,0,5],[1,0,1,5],[2,0,2,5],[3,0,3,5],[4,0,4,5],[7,0,7,4]]}
["Inexhaustible Exam-Style Practice"]
["Based on Problem 9(a) - Spring 2011 CAS Exam 7"]
["Let C = the incremental claim amount in question. "]
["Let D = the prior cumulative development."]
["Let λ = the loss-development factor for the time increment in question."]
[]
["Here λ is for the time period between ",null,null,{"$f":"Problem!C19","v":12},"and ",{"$f":"Problem!E19","v":24},"months."]
["Thus, λ (volume-weighted) is",null,null,null,null,{"$f":"IF(D7=12,Generation!C3, IF(D7=24,Generation!C4, IF(D7=36,Generation!C5,Generation!C6)))","v":1.6184218914223338}]
[]
["Here, D = ",null,null,{"$f":"IF(Problem!D22<0.1,Problem!B10, IF(Problem!D22<0.2, Problem!C10, IF(Problem!D22<0.3,Problem!D10, IF(Problem!D22<0.4, Problem!E10, IF(Problem!D22<0.5,Problem!B11, IF(Problem!D22<0.6, Problem!C11, IF(Problem!D22<0.7,Problem!D11, IF(Problem!D22<0.8, Problem!B12, IF(Problem!D22<0.9, Problem!C12, Problem!B13)))))))))","v":3306.0090193295664}]
[null,"         Here, φ =",null,{"$f":"Problem!F16","v":3.3914400529861455}]
[null,"E[C] = (λ-1)*D = ",null,{"$f":"(F8-1)*D10","v":2044.5083507930856},"  <<<< ANSWER FOR THE MEAN"]
[null,"Var[C] = φ*λ*(λ-1)*D = ",null,{"$f":"D11*F8*D12","v":11221.858232792927},"  <<<< ANSWER FOR THE VARIANCE"]

{"sheet":"Generation","index":2,"n_rows":6,"n_cols":3,"rows_kept":6,"cut":false,"hidden":false,"merged":[]}
[]
[null,"LDFs"]
[null,"12 to 24",{"$f":"SUM(Problem!C10:'Problem'!C13)/SUM(Problem!B10:'Problem'!B13)","v":1.6184218914223338}]
[null,"24 to 36",{"$f":"SUM(Problem!D10:'Problem'!D12)/SUM(Problem!C10:'Problem'!C12)","v":1.0928588494696982}]
[null,"36 to 48",{"$f":"SUM(Problem!E10:'Problem'!E11)/SUM(Problem!D10:'Problem'!D11)","v":1.0884454183354046}]
[null,"48 to 60",{"$f":"Problem!F10/Problem!E10","v":1.0173699179131577}]