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{"sheet":"Problem","index":0,"n_rows":22,"n_cols":6,"rows_kept":22,"cut":false,"hidden":false,"merged":[[20,0,21,2],[1,0,1,5],[0,0,0,5],[17,0,17,5],[16,0,16,5],[6,0,6,5],[4,0,4,5],[2,0,2,5],[3,0,3,5]]}
["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 10(a) and (c) - Spring 2011 CAS Exam 7"]
[]
["You are given the following information for a line of business for a reinsurance company as of December 31, 2044:"]
[]
["Calendar-Accident Year","Earned Risk Pure Premium","Adjusted Premium","Aggregate Reported Loss","Aggregate Loss Report Lag","Chain-Ladder IBNR"]
[2039,{"$f":"25626*D22+1000","v":14669.523931741714},{"$f":"1.07*B10","v":15696.390606963636},{"$f":"0.81*C10+124","v":12838.076391640547},{"$f":"1-0.1*D22","v":0.94665759801864624},{"$f":"2150*D22","v":1146.8616425991058}]
[2040,{"$f":"15125*D22+6697","v":14765.038299679756},{"$f":"1.07*B11","v":15798.59098065734},{"$f":"0.14*C11+8000*D22","v":6479.1948958003286},{"$f":"1-0.2*D22-0.02","v":0.87331519603729246},{"$f":"4*F10-240*D22","v":4459.4248056411743}]
[2041,{"$f":"15150*(1-D22)+2000/D22","v":10817.988568914909},{"$f":"1.07*B12","v":11575.247768738953},{"$f":"7776-5400*(1-D22)","v":5256.489706993103},{"$f":"1-0.3*D22-0.01","v":0.82997279405593871},{"$f":"8899*D22-95","v":4651.9403523206711}]
[2042,{"$f":"88950*D22^2","v":25309.938398103266},{"$f":"1.07*B13","v":27081.634085970498},{"$f":"8240+21540*D22","v":19729.9533867836},{"$f":"1-0.4*D22-0.05","v":0.73663039207458492},{"$f":"41400*D22*(1-D22)","v":10303.749364839476}]
[2043,{"$f":"15210*D22*(1-D22)+13000","v":16785.507918821459},{"$f":"1.02*B14","v":17121.218077197889},{"$f":"12510-2510*D22","v":11171.105710268021},{"$f":"1-0.5*D22-0.1","v":0.63328799009323122},{"$f":"F13+2000*D22+250","v":11620.597404466551}]
[2044,{"$f":"21515-5160*D22","v":18762.532057762146},{"$f":"B15","v":18762.532057762146},{"$f":"16161+1360*D22-9900*(1-D22)^2","v":14731.294528605526},{"$f":"1-0.3-0.6*D22","v":0.3799455881118774},{"$f":"12500*(1+D22)-2500","v":16667.80024766922}]
["TOTAL ",{"$f":"SUM(B10:B15)","v":101110.52917502324},{"$f":"SUM(C10:C15)","v":106035.61357729047},{"$f":"SUM(D10:D15)","v":70206.114620091132},null,{"$f":"SUM(F10:F15)","v":48850.373817536194}]
["(a) Use the Stanard-Bϋhlmann method to estimate the total IBNR. "]
["(c) Use a credibility-weighted combination of the Stanard-Bϋhlmann and chain-ladder estimates with a linear function of the report lag as the credibility weight to calculate a total IBNR estimate. "]
[null,"For the chain-ladder estimate, use a credibility factor of ",null,null,null,{"$f":"D22","v":0.5334240198135376}]
[]
["TO RE-RANDOMIZE THE VALUES FOR THIS PROBLEM, CLICK ON THE FORMULA IN THE RED BOX AND PRESS \"ENTER\". That is all you need to do. "]
[null,null,null,{"$f":"StaticRand()","v":0.5334240198135376}]

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["Inexhaustible Exam-Style Practice"]
["Based on Problem 10(a) and (c) - Spring 2011 CAS Exam 7"]
["Solution (a)"]
["Stanard-Bϋhlmann Expected Loss Ratio (S-B ELR) = Total Reported Losses/∑[Adjusted Premium(k) * Report Lag(k)] for all years k under consideration. "]
[]
["Calendar-Accident Year","(1) Adjusted Premium","(2) Aggregate Loss Report Lag","(3) = (1)*(2) "]
[2039,{"$f":"Problem!C10","v":15696.390606963636},{"$f":"Problem!E10","v":0.94665759801864624},{"$f":"B7*C7","v":14859.107429550637}]
[2040,{"$f":"Problem!C11","v":15798.59098065734},{"$f":"Problem!E11","v":0.87331519603729246},13797.149579385765]
[2041,{"$f":"Problem!C12","v":11575.247768738953},{"$f":"Problem!E12","v":0.82997279405593871},9607.140732510039]
[2042,{"$f":"Problem!C13","v":27081.634085970498},{"$f":"Problem!E13","v":0.73663039207458492},19949.15473476889]
[2043,{"$f":"Problem!C14","v":17121.218077197889},{"$f":"Problem!E14","v":0.63328799009323122},10842.661784056549]
[2044,{"$f":"Problem!C15","v":18762.532057762146},{"$f":"Problem!E15","v":0.3799455881118774},7128.7412771543914]
[null,null,"TOTAL ",{"$f":"SUM(D7:D12)","v":76183.955537426271}]
[]
["S-B ELR = ",{"$f":"Problem!D16","v":70206.114620091132},"/",{"$f":"D13","v":76183.955537426271},"=",{"$f":"B15/D15","v":0.92153412256996226}]
["S-B IBNR (for all years) = (S-B ELR)*(Total Adjusted Premium) - (Total Reported Losses)  "]
["S-B IBNR = ",{"$f":"F15","v":0.92153412256996226},"*",{"$f":"Problem!C16","v":106035.61357729047},"-",{"$f":"Problem!D16","v":70206.114620091132},"=",{"$f":"B17*D17-F17","v":27509.321499024809}]
[null,null,null,null,null,null,null,"↑ ANSWER "]
["Solution (c)"]
["For each year, Credibility-Weighted IBNR = (Credibility Factor)*(Report Lag)*(Chain-Ladder IBNR) + [1 - (Credibility Factor)*(Report Lag)]*(S-B IBNR) "]
[]
["Calendar-Accident Year","(1) Credibility Factor","(2) Report Lag","(3) = (1)*(2)","(4) Chain-Ladder IBNR","(5) S-B IBNR = S-B ELR * (Adjusted Premium) * (1- Report Lag) ","(6) Credibility-Weighted IBNR = (3)*(4) + (1-(3))*(5)"]
[2039,{"$f":"Problem!F19","v":0.5334240198135376},{"$f":"Problem!E10","v":0.94665759801864624},{"$f":"B23*C23","v":0.50496990132213426},{"$f":"Problem!F10","v":1146.8616425991058},{"$f":"F15*Problem!C10*(1-C23)","v":771.58501823987865},{"$f":"D23*E23+(1-D23)*F23","v":961.08841821106125}]
[2040,{"$f":"Problem!F19","v":0.5334240198135376},{"$f":"Problem!E11","v":0.87331519603729246},0.46584730243446015,{"$f":"Problem!F11","v":4459.4248056411743},{"$f":"F15*Problem!C11*(1-C24)","v":1844.396545595996},3062.6004063279224]
[2041,{"$f":"Problem!F19","v":0.5334240198135376},{"$f":"Problem!E12","v":0.82997279405593871},0.44272742414119221,{"$f":"Problem!F12","v":4651.9403523206711},{"$f":"F15*Problem!C12*(1-C25)","v":1813.6777907549811},3070.254463673341]
[2042,{"$f":"Problem!F19","v":0.5334240198135376},{"$f":"Problem!E13","v":0.73663039207458492},0.39293634485724738,{"$f":"Problem!F13","v":10303.749364839476},{"$f":"F15*Problem!C13*(1-C26)","v":6572.8231006579463},8038.8396298373409]
[2043,{"$f":"Problem!F19","v":0.5334240198135376},{"$f":"Problem!E14","v":0.63328799009323122},0.33781102537516716,{"$f":"Problem!F14","v":11620.597404466551},{"$f":"F15*Problem!C14*(1-C27)","v":5785.9038646061208},7756.9276720562366]
[2044,{"$f":"Problem!F19","v":0.5334240198135376},{"$f":"Problem!E15","v":0.3799455881118774},0.20267210292105628,{"$f":"Problem!F15","v":16667.80024766922},{"$f":"F15*Problem!C15*(1-C28)","v":10720.935179169883},11926.198828390414]
[null,null,null,null,null,"TOTAL ",{"$f":"SUM(G23:G28)","v":34815.909418496318}]
[null,null,null,null,null,null,"↑ ANSWER "]