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["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 2 - Spring 2011 CAS Exam 7"]
[]
["You are given the following loss-reserving information as of December 31, 2034:"]
[]
[null,"Accident Year","On-Level Earned Premium","Growth Function","Reported Losses"]
[null,2032,{"$f":"56300*D31","v":39722.324901819229},{"$f":"(30^C20)/(30^C20+E20^C20)","v":0.66333475809550901},{"$f":"C10*(0.25+D31)*0.6","v":22773.941228406326}]
[null,2033,{"$f":"43000+5600*D31","v":46951.066064834595},{"$f":"(18^C20)/(18^C20+E20^C20)","v":0.47749723691979434},{"$f":"C11*0.7-2000*(1-D31)","v":32276.841268539429}]
[null,2034,{"$f":"60000*(1-D31)+20000","v":37667.149305343628},{"$f":"(6^C20)/(6^C20+E20^C20)","v":0.14901549939276165},{"$f":"0.14*E10+0.25*5400*D31+0.3*C12","v":15440.985704209743}]
[]
["Parameter standard deviation for the total estimated unpaid claims is",null,null,null,{"$f":"900*(1-D31)+100","v":365.00723958015442}]
["The expected accident-year loss-emergence pattern (growth function) can be approximated by a loglogistic function of the form G(x│ω, θ) = (x^ω)/(x^ω + θ^ω), where x denotes time in months from the average accident date to the evaluation date, and G is the growth function describing cumulative percent reported."]
[]
[]
[]
["The maximum likelihood estimates of the parameters are "]
[null,"ω =",{"$f":"1+D31/1.4","v":1.5039625082697188},"θ =",{"$f":"D31*20+5","v":19.110950231552124}]
[]
["The actual incremental loss emergence follows an over-disersed Poisson distribution with scaling factor σ^2 = "]
[null,null,null,null,{"$f":"50*D31*(1-D31)+1","v":11.387511024212692}]
[]
["(a) Using a truncation point of ",null,{"$f":"IF(D31<0.25, 4, IF(D31<0.5, 5, IF(D31<0.75, 6, 7)))","v":6},"years, estimate the total unpaid claims using the Cape Cod method."]
[]
[]
["(b) Calculate the coefficient of variation of the total unpaid claims estimated in part (a) above. "]
[]
["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":0.7055475115776062}]

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["Inexhaustible Exam-Style Practice"]
["Based on Problem 2 - Spring 2011 CAS Exam 7"]
["Solution (a)"]
["Accident Year","(1) On-Level Earned Premium","(2) Age at 12/31/2034","(3) Average Age","(4) Growth Function","(5) = (1)*(4) = (On-Level Earned Premium) * (Growth Function)","(6) Reported Losses","(7) Expected Loss Ratio = ELR = (Sum of (6))/(Sum of (5)"]
[2032,{"$f":"Problem!C10","v":39722.324901819229},36,30,{"$f":"Problem!D10","v":0.66333475809550901},{"$f":"B5*E5","v":26349.198779739472},{"$f":"Problem!E10","v":22773.941228406326}]
[2033,{"$f":"Problem!C11","v":46951.066064834595},24,18,{"$f":"Problem!D11","v":0.47749723691979434},{"$f":"B6*E6","v":22419.00431639724},{"$f":"Problem!E11","v":32276.841268539429}]
[2034,{"$f":"Problem!C12","v":37667.149305343628},12,6,{"$f":"Problem!D12","v":0.14901549939276165},{"$f":"B7*E7","v":5612.9890644374955},{"$f":"Problem!E12","v":15440.985704209743}]
["TOTAL",{"$f":"SUM(B5:B7)","v":124340.54027199745},null,null,null,{"$f":"SUM(F5:F7)","v":54381.19216057421},{"$f":"SUM(G5:G7)","v":70491.768201155501},{"$f":"G8/F8","v":1.2962527190101083}]
[]
[null,"(8) Years at Truncation Point","(9) Age in Months at Truncation Point","(10) Average Age in Months at Truncation Point = (9) - 6"]
[null,{"$f":"Problem!C25","v":6},{"$f":"B11*12","v":72},{"$f":"C11-6","v":66}]
[null,null,null,"ω =",{"$f":"Problem!C20","v":1.5039625082697188},"θ =",{"$f":"Problem!E20","v":19.110950231552124}]
["Growth function for truncation = (x^ω)/(x^ω + θ^ω), where x is the average age in months at truncation point. "]
["Growth function for truncation =",null,{"$f":"(D11^E12)/(D11^E12+G12^E12)","v":0.86576261560811585}]
[]
["Accident Year","(10) Growth Function for Truncation Point - Growth Function at 12/31/2034","Estimated Reserves = (1)*(7)*(10)"]
[2032,{"$f":"C14-E5","v":0.20242785751260683},{"$f":"B5*H8*B17","v":10423.045131965877}]
[2033,{"$f":"C14-E6","v":0.38826537868832151},{"$f":"B6*H8*B18","v":23630.004519830432}]
[2034,{"$f":"C14-E7","v":0.71674711621535425},{"$f":"B7*H8*B19","v":34995.998412800451}]
["TOTAL",null,{"$f":"SUM(C17:C19)","v":69049.048064596762}," <<< ANSWER"]
[]
["Solution (b) "]
["Process Variance = (σ^2)*E(Reserves) = ",null,{"$f":"Problem!E23","v":11.387511024212692},"*",{"$f":"C20","v":69049.048064596762},"=",{"$f":"C23*E23","v":786296.79604698764}]
["Parameter Variance = (Parameter Standard Deviation)^2 =",null,null,{"$f":"Problem!E14","v":365.00723958015442},"^2 =",null,{"$f":"D24^2","v":133230.28494592424}]
[null,null,"Total Variance = Process Variance + Parameter Variance = ",null,null,null,{"$f":"G23+G24","v":919527.08099291194}]
[null,null,"Total Standard Deviation = (Total Variance)^0.5 = ",null,null,null,{"$f":"G25^0.5","v":958.91974689903634}]
[null,null,"Coefficient of Variation = (Total Standard Deviation)/(E(Reserves))",null,null,null,{"$f":"G26/C20","v":1.3887515813425086E-2},"<<< ANSWER"]