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{"sheet":"Problem","index":0,"n_rows":19,"n_cols":8,"rows_kept":19,"cut":false,"hidden":false,"merged":[[12,0,12,1],[17,0,18,2],[1,0,1,5],[2,0,2,5],[3,0,3,5],[4,0,4,5],[0,0,0,6],[5,0,5,8],[6,0,6,1],[6,2,6,4],[6,5,6,7]]}
["Free Practice Problems for Society of Actuaries (SOA) Exam GIADV: Advanced Topics in General Insurance"]
["G. Stolyarov II, ASA, ACAS, MAAA, CPCU, ARe, ARC, API, AIS, AIE, AIAF"]
["http://www.rationalargumentator.com/index/giadv-study-guide/"]
["Inexhaustible Exam-Style Practice"]
["Based on Problem 7(b) - Spring 2014 SOA Exam GIADV"]
["You are evaluating the renewal of two accounts, X and Y, which are exposed to two possible independent claim events, 1 and 2. The following information is given:"]
["Event (i)",null,"Loss for Account (L)",null,null,"(L^2)*p*(1-p)"]
["i","p(i)","X","Y","X+Y","X","Y","X+Y"]
[1,{"$f":"ROUND(D19/10,3)","v":5.2999999999999999E-2},{"$f":"ROUND(2000*D19+15000/D19,0)","v":29187},{"$f":"ROUND(MAX(96000*D19+18000/D19-2200, 1000), 0)","v":82753},{"$f":"SUM(C9:D9)","v":111940},{"$f":"(C9^2)*B9*(1-B9)","v":42756757.715079002},{"$f":"(D9^2)*B9*(1-B9)","v":343710929.72071898},{"$f":"(E9^2)*B9*(1-B9)","v":628921517.64759994}]
[2,{"$f":"MAX(ROUND(0.005+(0.1-D19/10)-0.001/D19,3), 0.001)","v":0.05},{"$f":"ROUND(100000*D19,0)","v":53342},{"$f":"ROUND(1000*D19+25000+5000/D19,0)","v":34907},{"$f":"SUM(C10:D10)","v":88249},{"$f":"(C10^2)*B10*(1-B10)","v":135155025.79000002},{"$f":"(D10^2)*B10*(1-B10)","v":57878685.827500001},{"$f":"(E10^2)*B10*(1-B10)","v":369924585.04750001}]
[]
["p(i) represents the probability of Event i."]
["The risk-load multiplier, λ, is",null,{"$f":"ROUND(D19/30000,7)","v":1.7799999999999999E-5},"."]
[]
["(b) Calculate the risk load for each account using the Shapley method."]
[]
[]
["TO RE-RANDOMIZE THE VALUES FOR THIS PROBLEM, CLICK ON THE FORMULA IN THE RED BOX AND PRESS \"ENTER\". That is all you need to do. "]
[null,null,null,{"$f":"StaticRand()","v":0.5334240198135376}]

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["Inexhaustible Exam-Style Practice"]
["Based on Problem 7(b) - Spring 2014 SOA Exam GIADV"]
["Part (b)"]
["We first calculate the variances of X, Y, and (X + Y). These are equal to the respective sums of (L^2)*p*(1-p) across all events."]
[]
[null,"(L^2)*p*(1-p)"]
[null,"X","Y","X+Y"]
[null,{"$f":"Problem!F9","v":42756757.715079002},{"$f":"Problem!G9","v":343710929.72071898},{"$f":"Problem!H9","v":628921517.64759994}]
[null,{"$f":"Problem!F10","v":135155025.79000002},{"$f":"Problem!G10","v":57878685.827500001},{"$f":"Problem!H10","v":369924585.04750001}]
["SUM = Variance",{"$f":"SUM(B8:B9)","v":177911783.50507903},{"$f":"SUM(C8:C9)","v":401589615.54821897},{"$f":"SUM(D8:D9)","v":998846102.69509995}]
[]
["We know that Var(X+Y) = Var(X) + Var(Y) + 2*Cov(X+Y), implying that Cov(X+Y) = (Var(X+Y)-Var(X)-Var(Y))/2 = "]
[null,null,"Cov(X+Y) = ",{"$f":"0.5*(D10-B10-C10)","v":209672351.82090098}]
["The Shapley Method allocates covariance equally among the accounts, meaning that each account gets a contribution of Cov(X+Y) to the risk load."]
["We recall that the risk-load coefficient λ =",null,{"$f":"Problem!C13","v":1.7799999999999999E-5}]
["The risk load for X = λ*(Var(X) + Cov(X+Y)) =",null,{"$f":"C15*(B10+D13)","v":6898.9976088024441},"←ANSWER for risk load for X"]
["The risk load for Y = λ*(Var(Y) + Cov(X+Y)) =",null,{"$f":"C15*(C10+D13)","v":10880.463019170333},"←ANSWER for risk load for Y"]