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{"sheet":"Problem","index":0,"n_rows":22,"n_cols":4,"rows_kept":22,"cut":false,"hidden":false,"merged":[[12,0,12,2],[13,0,13,2],[14,0,14,2],[15,0,15,2],[20,0,21,2],[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 6(a) and (b) - Spring 2011 CAS Exam 7"]
[]
["You are given the following information for accident year 2034 workers' compensation business with a $500,000 deductible as of December 31, 2036."]
[]
[null,"Ground-Up Reported Losses","Ground-Up Reported Severity","36-Months-to-Ultimate LDF"]
["Limited to $500,000",{"$f":"Generation!C4","v":3682009.3393325806},{"$f":"Generation!C5","v":11157.604058583578},{"$f":"Generation!C3","v":1.3640186786651611}]
["Unlimited",{"$f":"Generation!D4","v":3993892.514705658},{"$f":"Generation!D5","v":15975.570058822632},{"$f":"Generation!D3","v":1.7449297273860258}]
[]
["Full-coverage premium for all policies:",null,null,{"$f":"Generation!E7","v":15967447.840610405}]
["Full-coverage expected loss ratio:",null,null,{"$f":"Generation!E8","v":0.85439252853393555}]
["Excess ratio (per-occurrence charge):",null,null,{"$f":"Generation!E9","v":0.18701615517495962}]
["Excess ratio (aggregate charge):",null,null,{"$f":"Generation!E10","v":8.9037384986877452E-2}]
[]
["Problem (a)","Estimate the IBNR for losses above the deductible using the direct development method."]
["Problem (b)","Estimate the IBNR for losses above the deductible using the Bornhuetter-Ferguson method."]
[]
["TO RE-RANDOMIZE THE VALUES FOR THIS PROBLEM, CLICK ON THE FORMULA IN THE RED BOX AND PRESS \"ENTER\". That is all you need to do. "]
[null,null,null,{"$f":"StaticRand()","v":0.36401867866516113}]

{"sheet":"Solution","index":1,"n_rows":17,"n_cols":8,"rows_kept":17,"cut":false,"hidden":false,"merged":[[0,0,0,5],[1,0,1,5],[2,0,2,1],[10,0,10,1],[13,0,14,8]]}
["Inexhaustible Exam-Style Practice"]
["Based on Problem 6(a) and 6(b) - Spring 2011 CAS Exam 7"]
["Solution (a)"]
["Excess Losses = Unlimited Losses - Limited Losses = ",null,null,null,null,{"$f":"Problem!B11-Problem!B10","v":311883.17537307739}]
["We find the Excess LDF."]
["(Unlimited Loss)*(Unlimited LDF) = (Limited Loss)*(Limited LDF) + (Excess Loss)*(Excess LDF)"]
["Excess LDF = [(Unlimited Loss)*(Unlimited LDF) -  (Limited Loss)*(Limited LDF)]/(Excess Loss) = "]
["Excess LDF = ",null,null,null,null,{"$f":" (Problem!B11*Problem!D11 - Problem!B10*Problem!D10)/F4","v":6.241863674424005}]
["Excess IBNR = (Reported Excess Losses)*(Excess LDF - 1) = ",null,null,null,null,{"$f":"F4*(F8-1)","v":1634849.0876521459},"<<<<<<<<  ANSWER"]
[]
["Solution (b)"]
["For the Bornhuetter-Ferguson (B-F) Method, IBNR = (Expected Loss)*(% Loss Unreported)"]
["% Excess Loss Unreported  = 1 - 1/(Excess LDF) = ",null,null,null,null,{"$f":"1-1/F8","v":0.83979143855744665}]
["Expected Excess Loss = (Full-Coverage Premium)*(Full-Coverage Loss Ratio)*[(Per-Occurrence Charge) + (1 - Per-Occurrence Charge)*(Aggregate Charge)]"]
[]
["Expected Excess Loss =",null,null,null,null,{"$f":"Problem!D13*Problem!D14*(Problem!D15+(1-Problem!D15)*Problem!D16)","v":3538885.0300646131}]
["B-F IBNR = ",{"$f":"F16","v":3538885.0300646131},"*",{"$f":"F13","v":0.83979143855744665},"=",{"$f":"F16*F13","v":2971925.3502873741},"<<<<<<<<  ANSWER","<<<<<<<<  ANSWER"]

{"sheet":"Generation","index":2,"n_rows":10,"n_cols":5,"rows_kept":10,"cut":false,"hidden":false,"merged":[[6,1,6,3],[7,1,7,3],[8,1,8,3],[9,1,9,3]]}
[]
[null,null,"Limited","Unlimited"]
[null,"36-Months-to-Ultimate LDF",{"$f":"1+Problem!D22","v":1.3640186786651611},{"$f":"1+3.131*Problem!D22/1.53","v":1.7449297273860258}]
[null,"Ground-Up Reported Losses",{"$f":"3500000+500000*Problem!D22","v":3682009.3393325806},{"$f":"3750000+670000*Problem!D22","v":3993892.514705658}]
[null,"Ground-Up Reported Severity",{"$f":"C4/330","v":11157.604058583578},{"$f":"D4/250","v":15975.570058822632}]
[]
[null,"Full-coverage premium for all policies:",null,null,{"$f":"10000000+1300000*Problem!D22+2000000/Problem!D22","v":15967447.840610405}]
[null,"Full-coverage expected loss ratio:",null,null,{"$f":" 1 - 0.4*Problem!D22","v":0.85439252853393555}]
[null,"Excess ratio (per-occurrence charge):",null,null,{"$f":"0.05+0.15*Problem!D22+0.03/Problem!D22","v":0.18701615517495962}]
[null,"Excess ratio (aggregate charge):",null,null,{"$f":"0.14-0.14*Problem!D22","v":8.9037384986877452E-2}]