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{"sheet":"Instructions","index":0,"n_rows":32,"n_cols":1,"rows_kept":32}
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["Instructions"]
[]
["1.) Find a quiet place and allow yourself the full four hour exam period to practice. Treat this just as you would the real exam."]
[]
["2.) Use the Navigator worksheet to see a brief description of each question, its point value and navigate between questions in your preferred order."]
[]
["3.) Answer each question either to the side or below the grey question area."]
[]
["4.) Use cell B1 on each question worksheet to mark whether you finished the question or not. You should use this feature to"]
["       reflect your confidence in your answer. This way you'll know if you're on the money or your guesses were lucky."]
[]
["5.) Grade each question harshly. It's better to put in extra reviewing time now than find the examiners aren't as generous as you hoped."]
["       Use increments of 0.25 when scoring; pay attention to the language used in the question and the point value. An \"identify\" question"]
["       is likely 0.25 per item while an \"explain\" or \"briefly justify\" gets 0.25 for the item and another 0.25 for the justification."]
[]
["6.) Enter your estimated score for each sub-part of a question in the box beneath the sub-part point value. They look like:"]
[]
["7.) Use the Point Grid to see your score and a breakdown of where you scored well and where you didn't."]
[]
["8.) Find the top five questions where you lost the most points. These are the topics you need to review the most intensely in the"]
["      next day or so."]
[]
["9.) On the BattleActs site → Custom Battles → BattleCards - Prior Exams → Select this exam and mark the cards you got right and wrong."]
["      This allows your Battle Readiness Quotient (BRQ) to track your strengths and weaknesses."]
[]
["10.) Use the Reset Exam button on the Point Grid worksheet to clear all of your work ready for a new attempt at this exam later."]
["slay the beast"]

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["Practice Exam 2 – Exam 8"]
[null,"Total Point Value","Sub-Part of Question",{"$nulls":8},"Your Score","Sub-Part of Question"]
["Question",null,"(a)","(b)","(c)","(d)","(e)","(f)","(g)","Status",null,"Question","(a)","(b)","(c)","(d)","(e)","(f)","(g)"]
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[2,{"$f":"SUM(C9:I9)","v":2.75},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},0.75,{"$nulls":4},{"$f":"INDIRECT(\"'\"&A9&\"'!B1\")","v":"Incomplete"},null,{"$f":"A9","v":2},"","","","","","",""]
[3,{"v":2.5,"d":"2.50"},{"v":2,"d":"2.00"},{"v":0.5,"d":"0.50"},{"$nulls":5},"Incomplete",null,3,"","","","","","",""]
[4,{"v":2,"d":"2.00"},{"v":1.5,"d":"1.50"},{"v":0.5,"d":"0.50"},{"$nulls":5},"Incomplete",null,4,"","","","","","",""]
[5,4.25,0.75,{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"v":0.5,"d":"0.50"},{"v":1,"d":"1.00"},null,null,"Incomplete",null,5,"","","","","","",""]
[6,4.75,0.75,{"v":1,"d":"1.00"},{"v":0.5,"d":"0.50"},{"v":0.5,"d":"0.50"},1.25,0.75,null,"Incomplete",null,6,"","","","","","",""]
[7,2.75,0.75,{"v":2,"d":"2.00"},{"$nulls":5},"Incomplete",null,7,"","","","","","",""]
[8,{"v":3.5,"d":"3.50"},{"v":3,"d":"3.00"},{"v":0.5,"d":"0.50"},{"$nulls":5},"Incomplete",null,8,"","","","","","",""]
[9,{"v":3.5,"d":"3.50"},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"v":1.5,"d":"1.50"},{"$nulls":4},"Incomplete",null,9,"","","","","","",""]
[10,{"v":5.5,"d":"5.50"},{"v":2.5,"d":"2.50"},{"v":2.5,"d":"2.50"},{"v":0.5,"d":"0.50"},{"$nulls":4},"Incomplete",null,10,"","","","","","",""]
[11,{"v":3.5,"d":"3.50"},{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},{"v":0.5,"d":"0.50"},{"$nulls":4},"Incomplete",null,11,{"$f":"_xlfn.IFNA(IF(ISBLANK(INDEX(INDIRECT(\"'\"&$L18&\"'!$A:$A\"),MATCH(M$7,INDIRECT(\"'\"&$L18&\"'!$A:$A\"),0)+2)),\"\",INDEX(INDIRECT(\"'\"&$L18&\"'!$A:$A\"),MATCH(M$7,INDIRECT(\"'\"&$L18&\"'!$A:$A\"),0)+2)),\"\")","v":""},"","","","","",""]
[12,{"v":2,"d":"2.00"},{"v":2,"d":"2.00"},{"$nulls":6},"Incomplete",null,12,"","","","","","",""]
[13,{"v":4,"d":"4.00"},{"v":0.5,"d":"0.50"},{"v":1.5,"d":"1.50"},{"v":2,"d":"2.00"},{"$nulls":4},"Incomplete",null,13,"","","","","","",""]
[14,3.25,3.25,{"$nulls":6},"Incomplete",null,14,"","","","","","",""]
[15,{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"$nulls":5},"Incomplete",null,15,"","","","","","",""]
[16,{"v":2,"d":"2.00"},{"v":2,"d":"2.00"},{"$nulls":6},"Incomplete",null,16,"","","","","","",""]
[17,{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"$nulls":6},"Incomplete",null,17,"","","","","","",""]
[18,3.25,{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},0.25,{"$nulls":4},"Incomplete",null,18,"","","","","","",""]
[19,{"v":2.5,"d":"2.50"},{"v":1,"d":"1.00"},{"v":0.5,"d":"0.50"},{"v":1,"d":"1.00"},{"$nulls":4},"Incomplete",null,19,"","","","","","",""]
[20,2.75,0.75,{"v":0.5,"d":"0.50"},{"v":0.5,"d":"0.50"},{"v":1,"d":"1.00"},{"$nulls":3},"Incomplete",null,20,"","","","","","",""]
[21,{"$f":"SUM(C28:I28)","v":{"v":4,"d":"4.00"}},{"v":2.5,"d":"2.50"},{"v":1,"d":"1.00"},{"v":0.5,"d":"0.50"},{"$nulls":4},{"$f":"INDIRECT(\"'\"&A28&\"'!B1\")","v":"Incomplete"},null,{"$f":"A28","v":21},"","","","","","",""]
[]
["Total",{"$f":"SUM(B8:B28)","v":{"v":67.5,"d":"67.50"}},{"$nulls":9},"TOTAL",{"$f":"IF(SUM(IF(M8:S28=\"\",0,1))=0,\"\",SUM(M8:S28))","v":""},null,"Percentage:",{"$f":"IF(M30=\"\",\"\",M30/B30)","v":""}]
[]
[{"$nulls":11},"Passing Score:",{"$f":"MROUND(72%*B30,0.25)","v":{"v":48.5,"d":"48.50"}}]

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[]
[]
[]
[]
[]
["Navigator – Select a question to go to it"]
[]
["Question #",{"$nulls":6},"Status"]
["Q1 -- Mahler -- Shifting Risk Parameters -- 5.75 points",{"$nulls":6},{"$f":"'Point Grid'!J8","v":"Incomplete"}]
["Q2 -- Goldburd (GLM) -- GLM offsets -- 2.75 points",{"$nulls":6},{"$f":"'Point Grid'!J9","v":"Incomplete"}]
["Q3 -- Goldburd (GLM) -- Number of Parameters within a GLM -- 2.50 points",{"$nulls":6},{"$f":"'Point Grid'!J10","v":"Incomplete"}]
["Q4 -- Goldburd (GLM) -- Odds ratio -- 2.00 points",{"$nulls":6},{"$f":"'Point Grid'!J11","v":"Incomplete"}]
["Q5 -- Goldburd (GLM) -- Calculating with interactions -- 4.25 points",{"$nulls":6},{"$f":"'Point Grid'!J12","v":"Incomplete"}]
["Q6 -- Couret & Venter -- Estimate variances, credibilities, and expected claims -- 4.75 points",{"$nulls":6},{"$f":"'Point Grid'!J13","v":"Incomplete"}]
["Q7 -- ISO Rating -- Company Subject Loss Cost -- 2.75 points",{"$nulls":6},{"$f":"'Point Grid'!J14","v":"Incomplete"}]
["Q8 -- Fisher -- Quintiles & Efficiency Tests -- 3.50 points",{"$nulls":6},{"$f":"'Point Grid'!J15","v":"Incomplete"}]
["Q9 -- Fisher -- Experience & Schedule Rating -- 3.50 points",{"$nulls":6},{"$f":"'Point Grid'!J16","v":"Incomplete"}]
["Q10 -- NCCI Experience Rating -- Calculate experience modifications -- 5.50 points",{"$nulls":6},{"$f":"'Point Grid'!J17","v":"Incomplete"}]
["Q11 -- Bailey & Simon -- Single car-year credibility -- 3.50 points",{"$nulls":6},{"$f":"'Point Grid'!J18","v":"Incomplete"}]
["Q12 -- Fisher -- Balance Equations -- 2.00 points",{"$nulls":6},{"$f":"'Point Grid'!J19","v":"Incomplete"}]
["Q13 -- Fisher -- Tables M and L -- 4.00 points",{"$nulls":6},{"$f":"'Point Grid'!J20","v":"Incomplete"}]
["Q14 -- Fisher -- Large Dollar Deductible Premium -- 3.25 points",{"$nulls":6},{"$f":"'Point Grid'!J21","v":"Incomplete"}]
["Q15 -- Fisher -- Tables M and L -- 2.00 points",{"$nulls":6},{"$f":"'Point Grid'!J22","v":"Incomplete"}]
["Q16 -- Bahnemann -- Risk Loaded ILFs -- 2.00 points",{"$nulls":6},{"$f":"'Point Grid'!J23","v":"Incomplete"}]
["Q17 -- Bahnemann -- Excess Layer Inflation -- 1.00 point",{"$nulls":6},{"$f":"'Point Grid'!J24","v":"Incomplete"}]
["Q18 -- NCCI Retrospective Rating -- Preparation for Panjer's Recursive Algorithm -- 3.25 points",{"$nulls":6},{"$f":"'Point Grid'!J25","v":"Incomplete"}]
["Q19 -- Bahnemann -- Loss Elimination Ratios -- 2.50 points",{"$nulls":6},{"$f":"'Point Grid'!J26","v":"Incomplete"}]
["Q20 -- Bahnemann -- Inflation and the Pareto Distribution -- 2.75 points",{"$nulls":6},{"$f":"'Point Grid'!J27","v":"Incomplete"}]
["Q21 -- Holmes -- Interpreting a Lasso Credibility Model -- 4.00 points",{"$nulls":6},{"$f":"'Point Grid'!J28","v":"Incomplete"}]

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[{"$nulls":8},"a.)"]
["Points","A State Regulator is reviewing a Homeowners rate filing made by XYZ Insuance Company (XYZ)."]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('1'!A1,'Point Grid'!A:A,0))","v":5.75},"XYZ provided 15 years of historical data as of 12/31/2022 in support of their catastrophe provision:"]
[]
[null,"Accident","Earned","Case Incurred Loss and DCC ($000)"]
[null,"Year","Exposures","Catastrophic","Non-Catastrophic"]
[null,2007,{"v":2601,"d":"2,601"},0,{"v":14100,"d":"14,100"}]
[null,2008,{"v":7331,"d":"7,331"},0,{"v":25700,"d":"25,700"}]
[null,2009,{"v":14330,"d":"14,330"},{"v":10024,"d":"10,024"},{"v":30000,"d":"30,000"}]
[null,2010,{"v":17056,"d":"17,056"},0,{"v":27500,"d":"27,500"}]
[null,2011,{"v":19513,"d":"19,513"},{"v":10890.8,"d":"10,891"},{"v":32400,"d":"32,400"}]
[null,2012,{"v":22182,"d":"22,182"},0,{"v":43700,"d":"43,700"}]
[null,2013,{"v":26191,"d":"26,191"},{"v":62834,"d":"62,834"},{"v":48900,"d":"48,900"}]
[null,2014,{"v":36205,"d":"36,205"},0,{"v":56600,"d":"56,600"}]
[null,2015,{"v":37069,"d":"37,069"},{"v":45263.3,"d":"45,263"},{"v":58100,"d":"58,100"}]
[null,2016,{"v":38054,"d":"38,054"},{"v":87378.4,"d":"87,378"},{"v":79200,"d":"79,200"}]
[null,2017,{"v":38928,"d":"38,928"},{"v":60517,"d":"60,517"},{"v":82900,"d":"82,900"}]
[null,2018,{"v":41699,"d":"41,699"},{"v":12909,"d":"12,909"},{"v":87700,"d":"87,700"}]
[null,2019,{"v":44087,"d":"44,087"},{"v":185228.7,"d":"185,229"},{"v":91900,"d":"91,900"}]
[null,2020,{"v":45128,"d":"45,128"},{"v":117420.9,"d":"117,421"},{"v":93900,"d":"93,900"}]
[null,2021,{"v":44042,"d":"44,042"},{"v":179632.1,"d":"179,632"},{"v":96900,"d":"96,900"}]
[]
[null,{"v":1.6556371763675823,"d":"1.656"},"15-year straight average factor"]
[null,{"v":1.9164288509711265,"d":"1.916"},"10-year straight average factor"]
[null,{"v":1.8686490407364196,"d":"1.869"},"15-year exposure weighted average factor"]
[null,{"v":1.9797178502892394,"d":"1.980"},"10-year exposure weighted average factor"]
[]
[null,"• XYZ selected the 10-year exposure weighted average catastrophe provision, citing a recent "]
[null,"upward trend in the ratio of catastrophe to non-catastrophe claims."]
[]
["(a)","Apply Mahler's Chi-squared test with α = 0.1 to evaluate whether the catastrophe provision "]
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[null,"catastrophe losses. Explain whether you agree with XYZ's statement."]
[]
[null,"The actuary at the regulator wonders if the selected provision is too high."]
[null,"The latest available industry catastrophe provision (applied to non-CAT claims) is:",{"$nulls":4},{"v":1.85,"d":"1.850"}]
[]
[null,"The actuary uses the latest 10 years of data provided by XYZ and estimates the catastrophe to"]
[null,"non-catastrophe claims ratio by giving weight Z/3 to each of the preceding three years with the "]
[null,"complement being the industry ratio."]
[]
["(b)","Calculate the optimal credibility to the nearest 10% using the mean squared error criterion."]
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[]
[]
["(c)","Using the method from part (b) above, estimate the future catastrophe provision which would"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A47,'Point Grid'!$C$7:$I$7,0))","v":0.5},"apply to non-catastrophic losses and opine on the reasonableness of XYZ's proposed "]
[null,"catastrophe provision."]
[]
["(d)","The regulatory analyst's manager contends that insufficient consideration is given to older "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A51,'Point Grid'!$C$7:$I$7,0))","v":0.75},"historical data under the analysis used in part b.) above. "]
[null,"Identify what would likely happen if the analysis was repeated using more years of data in the "]
[null,"catastrophe provision (not more years of data when calculating the optimal credibility) and"]
[null,"briefly explain why."]

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[{"$nulls":8},"a.)"]
["Points","An analyst is building a generalized linear model for a rating plan. The new plan"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('2'!A1,'Point Grid'!A:A,0))","v":2.75},"will include the territory and deductible relativities from their existing  rating plan."]
[]
["(a)","Briefly describe how the analyst should incorporate territory and deductible into"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A6,'Point Grid'!$C$7:$I$7,0))","v":1},"the GLM and explain why they should do this for each."]
[]
[]
["(b)","The analyst is building a pure premium model using a log-link function."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A10,'Point Grid'!$C$7:$I$7,0))","v":1},"They want to verify their model is correctly incorporating the territory and deductible"]
[null,"relativities which are shown below:"]
[]
[null,"Record ID","Territory","Deductible"]
[null,1,"A",{"v":500,"d":"$500"}]
[null,2,"B",{"v":1000,"d":"$1,000"}]
[null,3,"C",{"v":2000,"d":"$2,000"}]
[null,4,"B",{"v":2000,"d":"$2,000"}]
[]
[null,"Territory","Relativity",null,"Deductible","Relativity"]
[null,"A",{"v":1,"d":"1.000"},null,{"v":500,"d":"$500"},{"v":1.1,"d":"1.100"}]
[null,"B",{"v":1.25,"d":"1.250"},null,{"v":1000,"d":"$1,000"},{"v":1,"d":"1.000"}]
[null,"C",{"v":0.8,"d":"0.800"},null,{"v":2000,"d":"$2,000"},{"v":0.75,"d":"0.750"}]
[]
[null,"Calculate the value for each record using the method you described in part (a) above"]
[null,"which will allow the analyst to verify if the GLM is correctly set up."]
[]
["(c)","Identify which of the following are key things to consider when the actuary is "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A28,'Point Grid'!$C$7:$I$7,0))","v":0.75},"designing the risk classes for use in the GLM."]
[null,"i.)   Practicality – can you place a risk in the correct class accurately and quickly?"]
[null,"ii.)  Acceptability to Sales Agents – will the variable reduce their bonuses?"]
[null,"iii.) Risk of adverse selection  – are the classes sufficiently homogeneous?"]
[null,"iv.) Credibility – is there sufficient data in each class?"]
[null,"v.) Speed to Market – can they bring the product to market quicker than expected?"]

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[{"$nulls":9},"a.)"]
["Points","You are given the following table for model selection:"]
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[{"$nulls":6},"Number of"]
[null,"Model",{"$nulls":3},"-2*ll","Parameters","AIC"]
[null,"Intercept + Age",{"$nulls":3},"A",5,435]
[null,"Intercept + Vehicle Body",{"$nulls":3},392,11,414]
[null,"Intercept + Age + Vehicle Value",{"$nulls":3},392,"X",446]
[null,"Intercept + Age + Vehicle Body + Vehicle Value",{"$nulls":3},"B","Y",501]
[]
["(a)","Calculate A, B, X, and Y."]
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[]
[]
["(b)","Briefly explain which model performs best according to the AIC measure."]
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[{"$nulls":8},"a.)"]
["Points","You are given the following information for a fitted GLM:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('4'!A1,'Point Grid'!A:A,0))","v":2}]
[null,"Response variable","Occurrence of Accidents"]
[null,"Response distribution","Binomial"]
[null,"Link","Logit"]
[]
[null,null,"Degrees of"]
[null,"Parameter"," Freedom"]
[null,"Intercept",1,"x"]
[]
[null,"Driver's Age",2]
[null,1,1,0.288]
[null,2,1,0.064]
[null,3,0,0]
[]
[null,"Area",2]
[null,"A",1,-0.036]
[null,"B",1,0.053]
[null,"C",0,0]
[]
[null,"Vehicle Body",2]
[null,"Truck",1,1.136]
[null,"Other",1,-0.371]
[null,"Sedan",0,0]
[]
[null,0.22,"The probability of a driver in age group 2, from area C "]
[null,null,"and with vehicle body type Other, having an accident."]
[]
["(a)","Calculate the odds ratio of a driver in age group 3, from area B, and with vehicle body"]
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[]
[]
["(b)","Briefly interpret the odds ratio derived in part (a) above."]
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[{"$nulls":7},"a.)"]
["Points","An actuary is working on a usage based insurance (UBI) program for a state's Private Passenger"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('5'!A1,'Point Grid'!A:A,0))","v":4.25},"Automobile market. They create a generalized linear model (GLM) to predict claim severity"]
[null,"by Daily Miles Driven (DMD), Vehicle Type, and Electric Vehicle Ind (EVInd)."]
[]
[null,"• Policies are effective for 6-months and the actuary uses data from 2017 through 2019."]
[null,"• Daily Miles Driven is a continuous variable with a base level of 20 miles per day."]
[null,"• Vehicle Type is a categorical variable with levels: Car, Truck, and Van."]
[null,"• Electric Vehicle Ind is a binary variable which classifies whether a vehicle is counted as"]
[null,"   an electric vehicle or not."]
[null,"• The log-link function is chosen."]
[null,"• An interaction variable is included as ln(DMD/20) for EVInd."]
[null,"• The model results are as follows:"]
[]
[null,null,"Parameter","Coefficient"]
[null,null,"Intercept",9.1198]
[null,null,"Vehicle Type: Truck",0.3012]
[null,null,"Vehicle Type: Van",0.7879]
[null,null,"EVInd",-0.0988]
[null,null,"ln(DMD/20)",0.4083]
[null,null,"EVInd: Yes, ln(DMD/20)",-0.0378]
[]
["(a)","Calculate the ratio of the estimated claim severity for an Electric Vehicle to that of a non-Electric "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A24,'Point Grid'!$C$7:$I$7,0))","v":0.75},"Vehicle for the following characteristics:"]
[]
[null,null,"Daily Miles Driven",30]
[null,null,"Vehicle Type","Truck"]
[]
["(b)","Suppose the median Daily Miles Driven for your book of business is estimated as 20 miles per day."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A30,'Point Grid'!$C$7:$I$7,0))","v":1},"Calculate the intercept term for a \"typical\" policyholder and briefly explain its meaning."]
[]
[]
["(c)","The actuary is considering adding Years of Driving Experience (YDE) to the model. "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A34,'Point Grid'!$C$7:$I$7,0))","v":1},"Describe how they can determine whether the interaction between ln(YDE) and ln(DMD/20)"]
[null,"is significant."]
[]
["(d)","Identify two limitations of Generalized Linear Models."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A38,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(e)","Briefly explain why each of the limitations in part b.) above may be present in the actuary's work."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A42,'Point Grid'!$C$7:$I$7,0))","v":1}]

{"sheet":"6","index":8,"n_rows":43,"n_cols":15,"rows_kept":43,"merged":[[0,11,0,12]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":6},"Incomplete",{"$nulls":9},"Navigator",null,null,"Solution"]
[{"$nulls":13},"a.)"]
["Points","An actuary has collected the following claim count data for Workers' Compensation claims."]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('6'!A1,'Point Grid'!A:A,0))","v":4.75},"The only injury types are Fatal, Major, and Temporary Total (TT)."]
[null,"The classes below are the only classes the company writes in Hazard Group F."]
[]
[null,null,"Year 1",null,null,"Year 2",null,null,"Total"]
[null,"Class","Fatal","Major","TT","Fatal","Major","TT","Fatal","Major","TT"]
[null,1,1,13,415,8,27,168,{"$f":"C9+F9","v":9},{"$f":"D9+G9","v":40},583]
[null,2,6,18,245,9,15,205,{"$f":"C10+F10","v":15},{"$f":"D10+G10","v":33},{"$f":"E10+H10","v":450}]
[null,3,6,25,499,1,27,435,7,52,934]
[null,"Hazard Group F",{"$f":"SUM(C9:C11)","v":13},{"$f":"SUM(D9:D11)","v":56},{"v":1159,"d":"1,159"},18,69,808,31,125,{"v":1967,"d":"1,967"}]
[]
[null,"Let V denote the ratio of Fatal claims to TT claims."]
[null,"Let X denote the ratio of Major claims to TT claims."]
[null,"Answer the following using Couret & Venter's multi-dimensional credibility technique."]
[]
["(a)","Calculate the estimated Expected Process Variance for X for the hazard group."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A18,'Point Grid'!$C$7:$I$7,0))","v":0.75}]
[]
[]
["(b)","Calculate the estimated Variance of Hypothetical Means for X for the hazard group."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A22,'Point Grid'!$C$7:$I$7,0))","v":1}]
[]
[]
["(c)","Calculate the estimated covariance between V and X for the hazard group."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A26,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
[null,"Given the following:"]
[null,"EPV V",{"v":0.10282227448621183,"d":"0.1028"}]
[null,"VHM V",{"v":0,"d":"0.0000"}]
[]
["(d)","Calculate the Variance of V and the Variance of X for Class 3."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A34,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(e)","Calculate the credibilities used by Class 3 to estimate X for its population."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A38,'Point Grid'!$C$7:$I$7,0))","v":1.25}]
[]
[]
["(f)","Calculate the expected number of Major claims for Class 3."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A42,'Point Grid'!$C$7:$I$7,0))","v":0.75}]

{"sheet":"7","index":9,"n_rows":48,"n_cols":14,"rows_kept":48,"merged":[[0,10,0,11],[42,2,43,2],[44,2,45,2],[46,2,47,2]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":7},"Incomplete",{"$nulls":8},"Navigator",null,null,"Solution"]
[{"$nulls":12},"a.)"]
["Points","The following policy is being rated using the ISO CGL rating plan."]
[{"$f":"INDEX('Point Grid'!B:B,MATCH(A1,'Point Grid'!A:A,0))","v":2.75},{"$nulls":5},"Current Company Rates per Exposure"]
[null,{"$f":"DATE(YEAR(TODAY()),12,1)","v":"2025-12-01"},"Effective Date",{"$nulls":3},"Policy Type","Sub-line","Rate"]
[null,"Claims-Made (CM)","Policy Type",{"$nulls":3},"3rd-yr CM","Prem/Ops",7.7]
[null,{"v":0.72,"d":"72%"},"Expected Loss Ratio (ELR)",{"$nulls":3},"3rd-yr CM","Products",8.9]
[{"$nulls":6},"2nd-yr CM","Prem/Ops",3.3]
[{"$nulls":6},"2nd-yr CM","Products",4.2]
[{"$nulls":6},"1st-yr CM","Prem/Ops",1.8]
[{"$nulls":6},"1st-yr CM","Products",4.1]
[{"$nulls":6},"Ocurrence","Prem/Ops",7.9]
[{"$nulls":6},"Ocurrence","Products",5.4]
[]
[null,"Information about previous policy years"]
[{"$nulls":4},"Policy","Gross",null,"Current Increased Limits Factors"]
[{"$nulls":4},"Limits","Annual",null,"Aggregate Limit"]
[null,"Effective Date","Policy Type",null,"(occ/agg)","Sales",null,"200k","250k","500k"]
[null,{"$f":"DATE(YEAR(TODAY())-1,12,1)","v":"2024-12-01"},"2nd-year Claims-Made",null,"250k/500k",{"v":108000,"d":"$108,000"},"100k",{"v":1,"d":"1.000"},{"v":1.35,"d":"1.350"},{"v":1.63,"d":"1.630"}]
[null,{"$f":"DATE(YEAR(TODAY())-2,12,1)","v":"2023-12-01"},"1st-year Claims-Made",null,"150k/500k",{"v":72000,"d":"$72,000"},"150k",{"v":1.15,"d":"1.150"},{"v":1.29,"d":"1.290"},{"v":1.81,"d":"1.810"}]
[null,{"$f":"DATE(YEAR(TODAY())-3,12,1)","v":"2022-12-01"},"Occurrence",null,"100k/250k",{"v":33000,"d":"$33,000"},"250k",{"v":1.33,"d":"1.330"},{"v":1.46,"d":"1.460"},{"v":1.95,"d":"1.950"}]
[null,{"$f":"DATE(YEAR(TODAY())-4,12,1)","v":"2021-12-01"},"Occurrence",null,"100k/200k",{"v":16000,"d":"$16,000"}]
[]
[]
["(a)","Briefly explain why the Company Subject Loss Cost should be calculated using the Historical Exposures at Present Company Rates "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A25,'Point Grid'!$C$7:$I$7,0))","v":0.75},"approach instead of the standard approach or the Present Average Company Rates approach."]
[]
[]
["(b)","Calculate the Company Subject Loss Cost using the Historical Exposures at Present Company Rates approach using the information"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A29,'Point Grid'!$C$7:$I$7,0))","v":2}," provided below."]
[null,null,"Table 13B"]
[null,null,"Sub-line","Occurrence","4th-yr CM","3rd-yr CM","2nd-yr CM","1st-yr CM"]
[null,null,"Prem/Ops",{"v":1,"d":"1.00"},1.14,{"v":1.2,"d":"1.20"},1.32,1.62]
[null,null,"Products",{"v":1,"d":"1.00"},1.51,1.59,2.03,2.39]
[]
[null,null,"Table 13C"]
[null,null,"Sub-line","Occurrence","4th-yr CM","3rd-yr CM","2nd-yr CM","1st-yr CM"]
[null,null,"Prem/Ops",{"v":1,"d":"1.00"},0.84,0.78,0.67,0.47]
[null,null,"Products",{"v":1,"d":"1.00"},0.49,0.43,0.35,0.22]
[]
[null,null,"Table 14"]
[null,null,"Year of Experience Period","Sub-line","Rule 5B","Rule 5C"]
[null,null,"Latest Year","Prem/Ops",0.907,0.926]
[{"$nulls":3},"Products",0.882,0.901]
[null,null,"2nd Latest Year","Prem/Ops",0.864,0.892]
[{"$nulls":3},"Products",0.828,0.854]
[null,null,"3rd Latest Year","Prem/Ops",0.823,0.858]
[{"$nulls":3},"Products",0.777,{"v":0.81,"d":"0.810"}]

{"sheet":"8","index":10,"n_rows":24,"n_cols":9,"rows_kept":24,"merged":[[0,5,0,6]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":8},"Incomplete",{"$nulls":3},"Navigator",null,null,"Solution"]
[{"$nulls":7},"a.)"]
["Points","The following information was taken from two different experience rating plans:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('8'!A1,'Point Grid'!A:A,0))","v":3.5},null,"Experience Mod",null,"Experience Data"]
[null,"Insured","Plan A","Plan B","Manual Premium ($)","Losses ($)"]
[null,1,0.62,0.66,{"v":100000,"d":"100,000"},{"v":65000,"d":"65,000"}]
[null,2,0.77,0.81,{"v":80000,"d":"80,000"},{"v":80000,"d":"80,000"}]
[null,3,0.92,0.96,{"v":100000,"d":"100,000"},{"v":95000,"d":"95,000"}]
[null,4,0.96,0.96,{"v":80000,"d":"80,000"},{"v":96000,"d":"96,000"}]
[null,5,{"v":1,"d":"1.00"},0.97,{"v":100000,"d":"100,000"},{"v":97000,"d":"97,000"}]
[null,6,1.03,1.02,{"v":80000,"d":"80,000"},{"v":102000,"d":"102,000"}]
[null,7,1.06,1.06,{"v":100000,"d":"100,000"},{"v":107000,"d":"107,000"}]
[null,8,{"v":1.1,"d":"1.10"},1.07,{"v":80000,"d":"80,000"},{"v":108500,"d":"108,500"}]
[null,9,1.14,1.08,{"v":100000,"d":"100,000"},{"v":110000,"d":"110,000"}]
[null,10,1.19,1.12,{"v":80000,"d":"80,000"},{"v":115000,"d":"115,000"}]
[]
[null,"All insureds are in the same industry. However, some are smaller firms than others."]
[]
["(a)","Demonstrate whether Plan A or Plan B appears to be more equitable according to:"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A19,'Point Grid'!$C$7:$I$7,0))","v":3},"   (i) the quintiles test"]
[null,"   (ii) the efficiency test"]
[]
["(b)","Briefly explain whether Plan A or Plan B gives too much credit for good experience."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A23,'Point Grid'!$C$7:$I$7,0))","v":0.5}]

{"sheet":"9","index":11,"n_rows":29,"n_cols":9,"rows_kept":29,"merged":[[0,5,0,6]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":9},"Incomplete",{"$nulls":3},"Navigator",null,null,"Solution"]
[{"$nulls":7},"a.)"]
["Points"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('9'!A1,'Point Grid'!A:A,0))","v":3.5}]
[]
["(a)","Identify and explain two goals of experience rating."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A6,'Point Grid'!$C$7:$I$7,0))","v":1}]
[]
[]
["(b)","Given the following Workers' Compensation information for a Construction company:"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A10,'Point Grid'!$C$7:$I$7,0))","v":1}]
[null,null,"Policy Year","Loss Experience","Manual Premium"]
[null,null,2017,{"v":1000000,"d":"1,000,000"},{"v":500000,"d":"500,000"}]
[null,null,2018,{"v":1100000,"d":"1,100,000"},{"v":800000,"d":"800,000"}]
[null,null,2019,{"v":1400000,"d":"1,400,000"},{"v":1200000,"d":"1,200,000"}]
[]
[null,"Assume:"]
[null,"   • The policy period being rated is January 1, 2021 to January 1, 2022."]
[]
[null,{"v":1100000,"d":"1,100,000"},"2021 indicated manual premium"]
[null,1.25,"2021 experience modification factor"]
[]
[null,"Discuss whether each of the two goals identified in part (a) above are fulfilled."]
[]
["(c)","The Construction company plans to add an on-site medical team in 2022. "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A25,'Point Grid'!$C$7:$I$7,0))","v":1.5},"Briefly discuss the potential impact of this to:"]
[null,"   (i) the experience modification for 2022"]
[null,"   (ii) the schedule modification for 2022"]
[null,"   (iii) the experience modification for 2024."]

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[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":10},"Incomplete",{"$nulls":4},"Navigator",null,null,"Solution"]
[{"$nulls":8},"a.)"]
["Points","Both Employer A and Employer B want to purchase Workers' Compensation insurance in Alabama."]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('10'!A1,'Point Grid'!A:A,0))","v":5.5},"The effective date is January 1, 2023 for each policy. The following information applies:"]
[]
[null,"Policy Effective Date","Months of Data","Subject Premium"]
[{"$nulls":3},"Employer A","Employer B"]
[null,"2022-01-01",12,{"v":4500,"d":"4,500"},{"v":3000,"d":"3,000"}]
[null,"2021-01-01",12,{"v":6000,"d":"6,000"},{"v":5000,"d":"5,000"}]
[null,"2020-01-01",12,{"v":5500,"d":"5,500"},{"v":5000,"d":"5,000"}]
[null,"2019-01-01",12,{"v":4500,"d":"4,500"},{"v":7000,"d":"7,000"}]
[null,"2018-01-01",12,{"v":10000,"d":"10,000"},{"v":10000,"d":"10,000"}]
[]
[null,"Expected Loss",null,{"v":19600,"d":"19,600"},{"v":20500,"d":"20,500"}]
[null,"Expected Excess Loss",null,{"v":16072,"d":"16,072"},{"v":15744,"d":"15,744"}]
[]
[null,"Historical Claim Data"]
[null,"Employer","Accident Date","Claim Amount","Claim Description"]
[null,"A","2020-07-01",{"v":8000,"d":"8,000"},"Med only"]
[null,"A","2019-05-23",{"v":160000,"d":"160,000"},"Wage loss"]
[null,"A","2018-03-28",{"v":400000,"d":"400,000"}," 3 claims from one occurrence - wage loss"]
[null,"B","2022-02-10",{"v":10000,"d":"10,000"},"Med only"]
[null,"B","2021-03-20",{"v":175000,"d":"175,000"},"Disease loss"]
[null,"B","2020-09-01",{"v":428000,"d":"428,000"},"4 claims from one occurrence - wage loss"]
[null,"B","2019-06-05",{"v":170000,"d":"170,000"},"Med only"]
[]
[null,"Use the NCCI's Experience Rating Plan Manual for Workers' Compensation and Employers Liability Insurance"]
[null,"to answer the following questions:"]
[]
["(a)","Demonstrate whether each employer qualifies for experience rating."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A30,'Point Grid'!$C$7:$I$7,0))","v":2.5}]
[]
[]
["(b)","For the employer(s) that qualify for experience rating, calculate the experience rating modification(s)."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A34,'Point Grid'!$C$7:$I$7,0))","v":2.5},"You may use the following tables:"]
[null,null,"State","Column A","Column B"]
[null,null,"AL",{"v":11000,"d":"11,000"},{"v":5500,"d":"5,500"}]
[null,null,"State table of Subject Premium Eligibility Amounts"]
[]
[null,null,{"v":5250,"d":"$5,250"},"AL Primary/Excess Split Point"]
[]
[null,null,"Expected Losses","Weighting Value"]
[null,null,"10,482 – 15,135",0.07]
[null,null,"15,136 – 19,890",0.08]
[null,null,"19,891 – 33,268",0.09]
[]
[null,null,"Expected Losses","Ballast Value"]
[null,null,"0 – 37,651",{"v":17500,"d":"17,500"}]
[null,null,"37,652 – 64,802",{"v":21000,"d":"21,000"}]
[]
[null,null,"G",null,7]
[null,null,"State Per Claim Accident Limit",null,{"v":175500,"d":"175,500"}]
[null,null,"State Multiple Claim Accident Limit",null,{"v":351000,"d":"351,000"}]
[]
["(c)","Given the payroll information below for Employer A and your result from part b.) above, determine the"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A55,'Point Grid'!$C$7:$I$7,0))","v":0.5},"standard premium for Employer A's policy effective January 1, 2023."]
[]
[null,{"v":7,"d":"$7.00"},"Employer A Manual Rate per $100 Payroll"]
[]
[null,"Policy Effective Date","Audited Payroll"]
[null,"2023-01-01",{"v":426000,"d":"426,000"},"(Estimated)"]
[null,"2022-01-01",{"v":419000,"d":"419,000"},"(Estimated)"]
[null,"2021-01-01",{"v":361000,"d":"361,000"}]
[null,"2020-01-01",{"v":330000,"d":"330,000"}]
[null,"2019-01-01",{"v":264000,"d":"264,000"}]
[null,"2018-01-01",{"v":184000,"d":"184,000"}]

{"sheet":"11","index":13,"n_rows":29,"n_cols":9,"rows_kept":29,"merged":[[0,5,0,6]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":11},"Incomplete",{"$nulls":3},"Navigator",null,null,"Solution"]
[{"$nulls":7},"a.)"]
["Points","The following data were compiled from ABC Insurance Company's portfolio of"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('11'!A1,'Point Grid'!A:A,0))","v":3.5},"Private Passenger Auto policies."]
[]
[null,"Group","Number of accident ","Earned Premium at ","Number of"]
[null,null,"free years","Present Group D","Claims "]
[{"$nulls":3},"Rates","Incurred"]
[null,"A",3,{"v":100000000,"d":"100,000,000"},{"v":120000,"d":"120,000"}]
[null,"B",2,{"v":10000000,"d":"10,000,000"},{"v":25000,"d":"25,000"}]
[null,"C",1,{"v":17000000,"d":"17,000,000"},{"v":44000,"d":"44,000"}]
[null,"D",0,{"v":10000000,"d":"10,000,000"},{"v":36000,"d":"36,000"}]
[]
["(a)","Calculate the credibility of a single car for each of the following ranges of accident-free years:"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A14,'Point Grid'!$C$7:$I$7,0))","v":2},"   i.) 1 or more"]
[null,"   ii.) 2 or more"]
[null,"   iii.) 3 or more"]
[]
["(b)","The following table provides the single car credibility for the XYZ automobile insurance portfolio:"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A19,'Point Grid'!$C$7:$I$7,0))","v":1},null,"Accident-Free Years","Single Car Credibility"]
[null,null,"3 or more",{"v":0.14,"d":"0.140"}]
[null,null,"2 or more",{"v":0.1,"d":"0.100"}]
[null,null,"1 or more",{"v":0.06,"d":"0.060"}]
[]
[null,"Discuss two conclusions which can be drawn from the different credibility results of the ABC"]
[null,"and XYZ portfolios."]
[]
["(c)","Explain why analysis of the two portfolios with different classification plans could assign "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A28,'Point Grid'!$C$7:$I$7,0))","v":0.5},"different values to the credibility of the experience of a single car."]

{"sheet":"12","index":14,"n_rows":18,"n_cols":8,"rows_kept":18,"merged":[[0,4,0,5]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":12},"Incomplete",null,null,"Navigator",null,null,"Solution"]
[{"$nulls":6},"a.)"]
["Points","Consider two policies:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('12'!A1,'Point Grid'!A:A,0))","v":2},"   • A retrospectively rated policy with no loss limit,"]
[null,"   • A retrospectively rated policy with a $500,000 loss limit."]
[]
[null,"Both policies are subject to the following parameters:"]
[]
[null,{"v":1,"d":"1.00"},"Maximum Premium Factor"]
[null,{"v":0.4,"d":"0.40"},"Minimum Premium Factor"]
[null,{"v":1.2,"d":"1.20"},"Loss Conversion Factor"]
[null,{"v":0.6,"d":"0.60"},"Expected Loss & ALAE Ratio"]
[null,1.05,"Tax Multiplier"]
[null,0.35,"Expense and Profit Provision"]
[null,{"v":0.1,"d":"0.10"},"Loss Elimination Ratio at $500,000"]
[]
["(a)","Calculate the difference between the balance equations for the two policies."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A17,'Point Grid'!$C$7:$I$7,0))","v":2}]

{"sheet":"13","index":15,"n_rows":32,"n_cols":8,"rows_kept":32,"merged":[[0,4,0,5]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":13},"Incomplete",null,null,"Navigator",null,null,"Solution"]
[{"$nulls":6},"a.)"]
["Points","The unlimited and limited loss ratios for 15 risks of "]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('13'!A1,'Point Grid'!A:A,0))","v":4},"approximately equal size are as follows:"]
[null,null,"Loss Ratio"]
[null,"Risk Number","Unlimited","Limited"]
[null,3,{"v":0.29,"d":"29%"},{"v":0.06,"d":"6%"}]
[null,4,{"v":0.35,"d":"35%"},{"v":0.06,"d":"6%"}]
[null,1,{"v":0.14,"d":"14%"},{"v":0.14,"d":"14%"}]
[null,2,{"v":0.25,"d":"25%"},{"v":0.25,"d":"25%"}]
[null,5,{"v":0.41,"d":"41%"},{"v":0.41,"d":"41%"}]
[null,8,{"v":0.63,"d":"63%"},{"v":0.41,"d":"41%"}]
[null,6,{"v":0.5,"d":"50%"},{"v":0.45,"d":"45%"}]
[null,7,{"v":0.5,"d":"50%"},{"v":0.5,"d":"50%"}]
[null,9,{"v":0.66,"d":"66%"},{"v":0.66,"d":"66%"}]
[null,13,{"v":0.99,"d":"99%"},{"v":0.67,"d":"67%"}]
[null,10,{"v":0.71,"d":"71%"},{"v":0.71,"d":"71%"}]
[null,11,{"v":0.75,"d":"75%"},{"v":0.75,"d":"75%"}]
[null,14,{"v":1,"d":"100%"},{"v":0.75,"d":"75%"}]
[null,12,{"v":0.96,"d":"96%"},{"v":0.96,"d":"96%"}]
[null,15,{"v":1,"d":"100%"},{"v":1,"d":"100%"}]
[]
["(a)","Calculate the loss elimination ratio."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A23,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(b)","Calculate the Table M charges at loss ratios from 0% to 100%"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A27,'Point Grid'!$C$7:$I$7,0))","v":1.5},"using increments of 10%."]
[]
[]
["(c)","Calculate the Table L charges at loss ratios from 0% to 100% "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A31,'Point Grid'!$C$7:$I$7,0))","v":2},"using increments of 10%."]

{"sheet":"14","index":16,"n_rows":24,"n_cols":11,"rows_kept":24,"merged":[[0,7,0,8]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":14},"Incomplete",{"$nulls":5},"Navigator",null,null,"Solution"]
[{"$nulls":9},"a.)"]
["Points","Given the following information:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('14'!A1,'Point Grid'!A:A,0))","v":3.25},null,null,"Ground-up"]
[null,null,"Percent of Claims","Loss per Claim"]
[null,null,{"v":0.45,"d":"45%"},{"v":22000,"d":"22,000"}]
[null,null,{"v":0.2,"d":"20%"},{"v":35000,"d":"35,000"}]
[null,null,{"v":0.15,"d":"15%"},{"v":150000,"d":"150,000"}]
[null,null,{"v":0.15,"d":"15%"},{"v":250000,"d":"250,000"}]
[null,null,{"v":0.05,"d":"5%"},{"v":1000000,"d":"1,000,000"}]
[]
[null,{"v":24793,"d":"$24,793"},"Full Coverage Premium"]
[null,{"v":0.59,"d":"59%"},"Expected Ground-up Loss Ratio"]
[null,{"v":0.1,"d":"10%"},"ALAE as a % of losses (assume the deductible doesn't apply to ALAE)"]
[null,{"v":0.04,"d":"4%"},"Incremental Fixed Expenses for processing a deductible (% of deductible losses)"]
[null,{"v":0.01,"d":"1%"},"Load for uncollectible deductible payments (% of deductible losses)"]
[null,{"v":0.08,"d":"8%"},"Profit Provision"]
[null,{"v":0.05,"d":"5%"},"Additional Risk Load (% of excess losses)"]
[null,{"v":0.1,"d":"10%"},"Commission"]
[null,{"v":0.05,"d":"5%"},"Other Variable Expenses"]
[null,{"v":100000,"d":"$100,000"},"Deductible"]
[]
["(a)","Calculate the final premium for a policy with a $100,000 deductible."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A23,'Point Grid'!$C$7:$I$7,0))","v":3.25}]

{"sheet":"15","index":17,"n_rows":39,"n_cols":9,"rows_kept":39,"merged":[[0,5,0,6]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":15},"Incomplete",{"$nulls":3},"Navigator",null,null,"Solution"]
[{"$nulls":7},"a.)"]
["Points","The diagram below exhibits cumulative distribution functions:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('15'!A1,'Point Grid'!A:A,0))","v":2},"   • F(y) represents aggregate loss ratios with no loss limit, and"]
[null,"   • F*(y) represents aggregate loss ratios adjusted for a per-occurrence loss limit."]
[]
[null,"The diagram is also partitioned into nine areas labeled with the letters from A to I."]
{"$rows_empty":22}
["(a)","Using the labels provided, give an algebraic expression for each of the following quantities:"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A30,'Point Grid'!$C$7:$I$7,0))","v":1},"   (i) The Table M Charge at rG"]
[null,"   (ii) The Table L Charge at rG"]
[null,"   (iii) The Table L Savings at rH"]
[null,"   (iv) The Loss Elimination Ratio"]
[]
["(b)","Using the labels provided and the entry ratio rG, algebraically demonstrate whether the"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A36,'Point Grid'!$C$7:$I$7,0))","v":1},"following equation is valid."]
[]
[null,"Table L Charge - Table M Charge = Table L Savings - Table M Savings"]

{"sheet":"16","index":18,"n_rows":18,"n_cols":9,"rows_kept":18,"merged":[[0,5,0,6]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":16},"Incomplete",{"$nulls":3},"Navigator",null,null,"Solution"]
[{"$nulls":7},"a.)"]
["Points","You believe the standard deviation of pure premiums is an appropriate measure of risk."]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('16'!A1,'Point Grid'!A:A,0))","v":2},"You are given the following pure premium distribution:"]
[]
[null,"Loss Amount","Probability"]
[null,{"v":0,"d":"$0"},{"v":0.9,"d":"90%"}]
[null,{"v":1000,"d":"$1,000"},{"v":0.09,"d":"9%"}]
[null,{"v":10000,"d":"$10,000"},{"v":0.01,"d":"1%"}]
[]
[null,{"v":0.1,"d":"10%"},"% of standard deviation of pure premium chosen as risk load"]
[null,{"v":2000,"d":"$2,000"},"Basic aggregate limit"]
[null,{"v":5000,"d":"$5,000"},"Aggregate limit on policy being priced"]
[]
[null,"You may assume there are no expenses."]
[]
["(a)","Calculate the increased limit factor with risk load for a $5,000 aggregate policy limit."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A17,'Point Grid'!$C$7:$I$7,0))","v":2}]

{"sheet":"17","index":19,"n_rows":18,"n_cols":8,"rows_kept":18,"merged":[[0,4,0,5]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":17},"Incomplete",null,null,"Navigator",null,null,"Solution"]
[{"$nulls":6},"a.)"]
["Points","An insurance company purchases Workers' Compensation excess of loss "]
[{"$f":"INDEX('Point Grid'!B:B,MATCH(VALUE('17'!A1),'Point Grid'!A:A,0))","v":1},"coverage of $500,000 per claim. Losses in the current year are as follows:"]
[]
[null,"Loss Number","Incurred Loss"]
[null,1,{"v":500000,"d":"500,000"}]
[null,2,{"v":600000,"d":"600,000"}]
[null,3,{"v":350000,"d":"350,000"}]
[null,4,{"v":1500000,"d":"1,500,000"}]
[null,5,{"v":950000,"d":"950,000"}]
[]
[null,{"v":500000,"d":"500,000"},"Retention"]
[null,{"v":500000,"d":"500,000"},"Limit"]
[null,{"v":0.09,"d":"9%"},"Inflation rate for Workers' Compensation claims"]
[]
["(a)","Calculate the inflation rate in the $500,000 excess of $500,000 layer."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A17,'Point Grid'!$C$7:$I$7,0))","v":1}]

{"sheet":"18","index":20,"n_rows":27,"n_cols":10,"rows_kept":27,"merged":[[0,6,0,7]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":18},"Incomplete",{"$nulls":4},"Navigator",null,null,"Solution"]
[{"$nulls":8},"a.)"]
["Points","Per-claim accident severity is modeled using a uniform distribution on the"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('18'!A1,'Point Grid'!A:A,0))","v":3.25},"interval [0, 18,000]."]
[]
["(a)","Using the equally spaced evaluation points of $3,000 calculate the probability density "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A6,'Point Grid'!$C$7:$I$7,0))","v":2},"function for a discrete version of this distribution for use in Panjer's recursive"]
[null," algorithm."]
[]
[null,"A multi-state, multi-hazard group policy is being priced using the following information:"]
[null,"Claim counts are modeled using a negative binomial distribution."]
[]
[null,null,"Hazard","Expected","Average "]
[null,"State","Group","Loss","Claim Size"]
[null,"AK","E",{"v":240000,"d":"240,000"},{"v":15000,"d":"15,000"}]
[null,"AL","G",{"v":171000,"d":"171,000"},{"v":9000,"d":"9,000"}]
[]
[null,"Variance-to-Mean relationships for claim count distributions:"]
[null,"VtMPC = 1 + 0.811265 * E[N]PC if E[N]PC ≤ 3.697927"]
[null,"VtMPC = 1.5 * (E[N]PC)0.75 if E[N]PC > 3.697927"]
[]
["(b)","Calculate the mean and variance-to-mean function for the expected claim counts on"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A22,'Point Grid'!$C$7:$I$7,0))","v":1},"a per-claim basis for use in Panjer's recursive algorithm."]
[]
[]
["(c)","Briefly describe an advantage of the NCCI Circular approach to produce the "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A26,'Point Grid'!$C$7:$I$7,0))","v":0.25},"Aggregate Loss Factors on Demand."]

{"sheet":"19","index":21,"n_rows":30,"n_cols":11,"rows_kept":30,"merged":[[0,7,0,8]]}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":19},"Incomplete",{"$nulls":5},"Navigator",null,null,"Solution"]
[{"$nulls":9},"a.)"]
["Points","An actuary is pricing a diminishing deductible which starts at $500 and ends "]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('19'!A1,'Point Grid'!A:A,0))","v":2.5},"at $1,500 using the following ground-up claims data:"]
[]
[null,null,"Claim #","Loss Size",null,"Claim #","Loss Size"]
[null,null,1,850,null,9,400]
[null,null,2,{"v":2250,"d":"2,250"},null,10,{"v":5000,"d":"5,000"}]
[null,null,3,{"v":1250,"d":"1,250"},null,11,{"v":1500,"d":"1,500"}]
[null,null,4,{"v":1000,"d":"1,000"},null,12,{"v":2000,"d":"2,000"}]
[null,null,5,{"v":2750,"d":"2,750"},null,13,100]
[null,null,6,500,null,14,900]
[null,null,7,250,null,15,{"v":1750,"d":"1,750"}]
[null,null,8,{"v":3500,"d":"3,500"}]
[]
["(a)","Calculate the loss elimination ratio which results from this diminishing"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A16,'Point Grid'!$C$7:$I$7,0))","v":1},"deductible."]
[]
[]
[null,"The underwriter responsible for this policy believes it is better for the"]
[null,"insurer to require a $1,500 franchise deductible than a $500 straight "]
[null,"deductible as the higher franchise deductible will eliminate more losses "]
[null,"than the straight deductible."]
[]
["(b)","Briefly explain why the underwriter is incorrect."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A25,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(c)","Give one reason in support of the franchise deductible and another "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$27,MATCH($A$1,'Point Grid'!$A$8:$A$27,0),MATCH(A29,'Point Grid'!$C$7:$I$7,0))","v":1},"reason in support of the straight deductible."]

{"sheet":"20","index":22,"n_rows":26,"n_cols":10,"rows_kept":26}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":20},"Incomplete",{"$nulls":5},"Navigator",null,"Solution"]
[{"$nulls":8},"a.)"]
["Points","An actuary is estimating the impact of inflation on their book of business."]
[2.75]
[null,"They model claim-size using a Pareto distribution with parameters:"]
[null,"α =",2]
[null,"β =",{"v":3000,"d":"3,000"}]
[]
[null,"Estimated Inflation",{"v":0.1,"d":"10%"}]
[null,"Exposure Growth",{"v":0.05,"d":"5%"}]
[]
["(a)","Calculate the expected excess severity for the layer 4,000 excess of 5,000."]
[0.75]
[]
[]
["(b)","Calculate the annual trend rate for claims in the layer 4,000 excess of 5,000."]
[0.5]
[]
[]
["(c)","Briefly describe why the annual trend rate is lower in part b.) above than the"]
[0.5,"estimated inflation chosen by the actuary."]
[]
[]
["(d)","Calculate the annual change in:"]
[1,"i.) Aggregate Loss"]
[null,"ii.) Aggregate Loss, due to claim-size inflation only"]

{"sheet":"21","index":23,"n_rows":45,"n_cols":10,"rows_kept":45}
[{"$f":"VALUE(MID(CELL(\"filename\",A1),FIND(\"]\",CELL(\"filename\",A1))+1,LEN(CELL(\"filename\",A1))-FIND(\"]\",CELL(\"filename\",A1))+1))","v":21},"Incomplete",{"$nulls":5},"Navigator",null,"Solution"]
[]
["Points","An actuary has built a GLM and a lasso credibility model and is evaluating the"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH(A1,'Point Grid'!A:A,0))","v":4},"model output for a categorical variable with five levels."]
[]
[null,"The complement of credibility for the lasso credibility model is the current"]
[null,"rating plan relativities which were previously produced by a GLM."]
[]
["(a)","Using the table and graph below, briefly explain the broad level of credibility"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$28,MATCH($A$1,'Point Grid'!$A$8:$A$28,0),MATCH(A9,'Point Grid'!$C$7:$I$7,0))","v":2.5},"assigned to each category by the lasso credibility model and explain"]
[null,"whether the results for categories A, D, and E are intuitive."]
{"$rows_empty":16}
[null,"Category","Exposures","GLM","Lasso Credibility","Complement"]
[null,"A",{"v":55000,"d":"55,000"},0.772,1.036,1.095]
[null,"B",{"v":175000,"d":"175,000"},1.952,1.881,1.881]
[null,"C",{"v":10000,"d":"10,000"},1.184,1.138,1.138]
[null,"D",{"v":48000,"d":"48,000"},0.723,0.801,1.043]
[null,"E",{"v":169000,"d":"169,000"},0.707,0.707,0.952]
[]
["(b)","Briefly describe two ways in which the actuary could address the "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$28,MATCH($A$1,'Point Grid'!$A$8:$A$28,0),MATCH(A35,'Point Grid'!$C$7:$I$7,0))","v":1},"counter-intuitive results identified in part a.) above."]
[]
[]
[null,"The actuary recently learned that the Data Enablement group who prepared the "]
[null,"data has grouped two sub-categories to form category D because "]
[null,"the prior model had shown these sub-categories were insignificant by "]
[null,"themselves. "]
[]
["(c)","Briefly explain whether or not this presents a problem when modeling"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$28,MATCH($A$1,'Point Grid'!$A$8:$A$28,0),MATCH(A44,'Point Grid'!$C$7:$I$7,0))","v":0.5},"using lasso credibility."]