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{"sheet":"Instructions","index":0,"n_rows":32,"n_cols":1,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
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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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["FORMULA SHEET"]
[]
["• For the negative binomial distribution (for use on question 3):"]
[]
[null,"○"]
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[]
[null,"○"]
[]
[]
["• For the shifted Pareto distribution (for use on questions 7, 13 & 15):"]
[]
[null,"○"]
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[]
[null,"○"]
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[]
[null,"○"]
[]
[]
[null,"○"]

{"sheet":"Point Grid","index":2,"n_rows":30,"n_cols":19,"rows_kept":30,"cut":false,"hidden":false,"merged":[[5,1,6,1]]}
[]
[]
[]
[]
["2019 Exam 8"]
[null,"Total Point Value","Sub-Part of Question",null,null,null,null,null,null,null,null,"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)"]
[1,{"$f":"SUM(C8:I8)","v":2.25},1.5,0.75,null,null,null,null,null,{"$f":"INDIRECT(\"'\"&A8&\"'!B1\")","v":"Incomplete"},null,{"$f":"A8","v":1},{"$f":"_xlfn.IFNA(IF(ISBLANK(INDEX(INDIRECT(\"'\"&$L8&\"'!$A:$A\"),MATCH(M$7,INDIRECT(\"'\"&$L8&\"'!$A:$A\"),0)+2)),\"\",INDEX(INDIRECT(\"'\"&$L8&\"'!$A:$A\"),MATCH(M$7,INDIRECT(\"'\"&$L8&\"'!$A:$A\"),0)+2)),\"\")","v":""},"","","","","",""]
[2,{"$f":"SUM(C9:I9)","v":2.75},1,0.75,1,null,null,null,null,{"$f":"INDIRECT(\"'\"&A9&\"'!B1\")","v":"Incomplete"},null,{"$f":"A9","v":2},"","","","","","",""]
[3,1.75,1.25,0.5,null,null,null,null,null,"Incomplete",null,3,"","","","","","",""]
[4,3,3,null,null,null,null,null,null,"Incomplete",null,4,"","","","","","",""]
[5,2.75,0.5,0.5,1.5,0.25,null,null,null,"Incomplete",null,5,"","","","","","",""]
[6,2,0.75,0.75,0.5,null,null,null,null,"Incomplete",null,6,"","","","","","",""]
[7,7.5,2.25,1.5,0.25,0.5,1.5,1,0.5,"Incomplete",null,7,"","","","","","",""]
[8,1.5,1.5,null,null,null,null,null,null,"Incomplete",null,8,"","","","","","",""]
[9,1,1,null,null,null,null,null,null,"Incomplete",null,9,"","","","","","",""]
[10,1.5,0.5,0.5,0.5,null,null,null,null,"Incomplete",null,10,"","","","","","",""]
[11,3.75,0.5,0.5,2.75,null,null,null,null,"Incomplete",null,11,{"$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":""},"","","","","",""]
[12,2,0.5,1,0.5,null,null,null,null,"Incomplete",null,12,"","","","","","",""]
[13,2,1.5,0.5,null,null,null,null,null,"Incomplete",null,13,"","","","","","",""]
[14,2,1,1,null,null,null,null,null,"Incomplete",null,14,"","","","","","",""]
[15,3.5,2,1,0.5,null,null,null,null,"Incomplete",null,15,"","","","","","",""]
[16,3,1.5,1.5,null,null,null,null,null,"Incomplete",null,16,"","","","","","",""]
[17,3,3,null,null,null,null,null,null,"Incomplete",null,17,"","","","","","",""]
[18,5.5,0.5,1,0.5,2,1,0.5,null,"Incomplete",null,18,"","","","","","",""]
[19,1.75,0.5,0.75,0.5,null,null,null,null,"Incomplete",null,19,"","","","","","",""]
[]
["Total",{"$f":"SUM(B8:B26)","v":52.5},null,null,null,null,null,null,null,null,null,"TOTAL",{"$f":"IF(SUM(IF(M8:S26=\"\",0,1))=0,\"\",SUM(M8:S26))","v":""},null,"Percentage:",{"$f":"IF(M28=\"\",\"\",M28/B28)","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Passing Score:",37]

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["Navigator – Select a question to go to it"]
[]
["Question #",null,null,null,null,null,null,"Status"]
["Q1 -- Couret & Venter -- Multi-Dimensional Credibility -- 2.25 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J8","v":"Incomplete"}]
["Q2 -- Goldburd (GLM) -- Model Validation -- 2.75 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J9","v":"Incomplete"}]
["Q3 -- Bailey & Simon -- Experience Modification -- 1.75 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J10","v":"Incomplete"}]
["Q4 -- Robertson -- Weighted k-means -- 3.00 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J11","v":"Incomplete"}]
["Q5 -- Goldburd (GLM) -- Logistic Models -- 2.75 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J12","v":"Incomplete"}]
["Q6 -- Goldburd (GLM) -- Interaction Terms --2.00 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J13","v":"Incomplete"}]
["Q7 -- Bahnemann -- Expected Ground Up Loss  (IQ) -- 7.50 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J14","v":"Incomplete"}]
["Q8 -- Bahnemann -- Excess Layer Premium -- 1.50 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J15","v":"Incomplete"}]
["Q9 -- Mahler -- When to Use Experience Rating -- 1.00 point",null,null,null,null,null,null,{"$f":"'Point Grid'!J16","v":"Incomplete"}]
["Q10 -- Fisher -- Quintiles & Efficiency Tests -- 1.50 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J17","v":"Incomplete"}]
["Q11 -- Fisher -- Experience Modification & Efficiency Test -- 3.75 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J18","v":"Incomplete"}]
["Q12 -- Fisher -- Table M -- 2.00 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J19","v":"Incomplete"}]
["Q13 -- Bahnemann -- Aggregate Loss in Layer -- 2.00 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J20","v":"Incomplete"}]
["Q14 -- Fisher -- Retrospective Rating -- 2.00 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J21","v":"Incomplete"}]
["Q15 -- Bahnemann -- Excess Severity -- 3.50 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J22","v":"Incomplete"}]
["Q16 -- Fisher -- Limited Table M -- 3.00 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J23","v":"Incomplete"}]
["Q17 -- Clark -- Technical Ratio -- 3.00 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J24","v":"Incomplete"}]
["Q18 -- Clark -- Property Per Risk Treaty (IQ) -- 5.50 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J25","v":"Incomplete"}]
["Q19 -- Grossi -- Quota Share Reinsurance -- 1.75 points",null,null,null,null,null,null,{"$f":"'Point Grid'!J26","v":"Incomplete"}]

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[1,"Incomplete",null,null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","An insurer uses five geographical Storm Zones (A, B, C, D, and E) in their rating plan."]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('1'!A1,'Point Grid'!A:A,0))","v":2.25},"The insurer refines their rating plan using the following approach:"]
[null,"• Divide each Storm Zone into numerous geographical sectors."]
[null,"• For each geographical sector and storm type, calculate the observed storm frequency"]
[null,"   as number of storms per year."]
[null,"   ○ There are three storm types defined as Moderate, Strong, and Severe storms."]
[]
[null,"The insurer performs two credibility procedures to produce estimates of the respective"]
[null,"storm frequencies in each sector. The first is a multi-dimensional credibility procedure"]
[null,"and the second is a single-dimensional credibility procedure (utilizing only a single"]
[null,"storm type)."]
[]
["(a)","The multi-dimensional credibility results for a particular sector in Storm Zone C for "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A15,'Point Grid'!$C$7:$I$7,0))","v":1.5},"Severe storms are given in the table below. The single-dimensional credibility factor"]
[null,"is 0.30."]
[null,"Storm Type","Coefficient","Storm Zone Mean Frequency",null,"Sector Mean Frequency"]
[null,"Intercept","not provided"]
[null,"Moderate",0.05,5.3,null,7.1]
[null,"Strong",0.12,1.4,null,2.4]
[null,"Severe",0.2,0.73,null,0.69]
[]
[null,"Calculate the mean frequency estimate of Severe storms for each of the two"]
[null,"credibility procedures."]
[]
["(b)","Fully explain why the single-dimensional credibility estimate in part (a) above is"]
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[2,"Incomplete",null,null,null,null,null,null,null,null,"Navigator",null,null,"Solution"]
[]
["Points","An actuary has built two generalized linear models to predict loss costs. Management has requested a series of model validation"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('2'!A1,'Point Grid'!A:A,0))","v":2.75},"plots to demonstrate the appropriateness of each of the new models. Output for each model, simple quantile plots, and a"]
[null,"double lift plot are shown below:"]
[null,null,null,"Observation","Actual Loss Cost","Model A Loss Cost","Model B Loss Cost","Earned Premium"]
[null,null,null,1,1500,825,900,1800]
[null,null,null,2,675,765,800,1450]
[null,null,null,3,0,615,350,2375]
[null,null,null,4,2250,900,3000,2625]
[null,null,null,5,5000,1050,3700,4875]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
[]
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[]
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[]
[]
[null,"Given the following:"]
[null,"• The actuary has already provided management with the simple quintile plots and the double lift chart shown above."]
[null,"• The company has implemented several segmented rate changes over the last three years."]
[]
["(a)","For each model, provide a loss ratio plot that management can use to assess lift. Identify the basis of sorting the data."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A41,'Point Grid'!$C$7:$I$7,0))","v":1}]
[]
[]
["(b)","Briefly describe one drawback of each type of model validation plot that the actuary has provided to management,"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A45,'Point Grid'!$C$7:$I$7,0))","v":0.75},"including the plot produced in part (a) above."]
[]
[]
["(c)","Using all three types of model validation plots provided to management, recommend which model should be "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A49,'Point Grid'!$C$7:$I$7,0))","v":1},"implemented. Do not perform any calculations."]

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[3,"Incomplete",null,null,"Formula Sheet",null,null,"Navigator",null,"Solution"]
[]
["Points","An insurance company has a private passenger auto book of business with an experience"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('3'!A1,'Point Grid'!A:A,0))","v":1.75},"modification factor in its rating plan."]
[null,"Given the following:"]
[null,"   • Annual claims for an individual driver follow a negative binomial distribution with "]
[null,"       r = 10."]
[null,"   • The expected claim frequency for the entire book of business is 0.101."]
[null,"   • The credibility for the group of risks that have had at least one accident in the last year"]
[null,"      is 0.02."]
[]
["(a)","Calculate the experience modification factor for a policy that has had at least one"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A12,'Point Grid'!$C$7:$I$7,0))","v":1.25},"accident in the last year."]
[]
[]
["(b)","Describe why a class with a higher volume of claims and more exposures may have less"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A16,'Point Grid'!$C$7:$I$7,0))","v":0.5},"credibility than a class with fewer claims and exposures."]

{"sheet":"4","index":7,"n_rows":20,"n_cols":9,"rows_kept":20,"cut":false,"hidden":false,"merged":[]}
[4,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","An actuary wants to cluster six workers compensation classes based on excess ratios at"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('4'!A1,'Point Grid'!A:A,0))","v":3},"two limits: 750,000 and 1,500,000. The actuary decides to use a weighted k-means"]
[null,"algorithm with three clusters. Given the following:"]
[null,"Class","On-Leveled Earned Premium","Normalized Excess Ratio at 750,000 Limit","Normalized Excess Ratio at 1,500,000 Limit","Initial Cluster"]
[null,1,7000000,0.25,9.5000000000000001E-2,"A"]
[null,2,8000000,0.2,0.08,"B"]
[null,3,7500000,0.17,6.2E-2,"C"]
[null,4,6000000,0.13,4.8000000000000001E-2,"A"]
[null,5,5000000,0.45,0.217,"A"]
[null,6,8500000,0.24,9.8000000000000004E-2,"B"]
[]
[null,"• At the start of the algorithm, the actuary randomly assigned each class to a cluster."]
[null,"• The actuary has observed that the 750,000 limit is selected by the insured 75% of the"]
[null,"    time, consistent across all six classes."]
[]
["(a)","Briefly justify which measure to use to calculate the distance between vectors and using"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A18,'Point Grid'!$C$7:$I$7,0))","v":3},"that measure, determine the cluster for each class after the first iteration of the "]
[null,"weighted k-means algorithm."]

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[5,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","The following confusion matrix shows the results from a claim fraud model with a "]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('5'!A1,'Point Grid'!A:A,0))","v":2.75},"discrimination threshold of 25%:"]
[null,null,"Predicted"]
[null,"Actual","Yes","No"]
[null,"Yes",72,162]
[null,"No",63,1203]
[]
["(a)","Identify a link function that can be used for a generalized linear model that has a binary"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A10,'Point Grid'!$C$7:$I$7,0))","v":0.5},"target variable and briefly explain why this link function is appropriate."]
[]
[]
["(b)","Calculate the sensitivity and specificity from the above data."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A14,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(c)","Plot the receiver operating characteristic (ROC) curve with the discrimination threshold"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A18,'Point Grid'!$C$7:$I$7,0))","v":1.5},"of 25%. Label each axis, the coordinates, and the discrimination thresholds of 100%, 25%"]
[null,"and 0% on the curve."]
[]
[null,"In addition, plot the ROC curve for each of the following two models:"]
[null,"    i. A model with no predictive power"]
[null,"  ii. A hypothetical \"perfect\" model"]
[]
["(d)","Briefly describe how the severity of claims will impact the selection of the model threshold."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A26,'Point Grid'!$C$7:$I$7,0))","v":0.25}]

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[6,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","An actuary creates a generalized linear model (GLM) to estimate commercial property claim"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('6'!A1,'Point Grid'!A:A,0))","v":2},"frequency by occupancy class and amount of insurance (AOI) for sprinklered and"]
[null,"non-sprinklered risks. Given the following:"]
[null,"   • Occupancy class is a categorical variable with four levels: Class 1, 2, 3 and 4."]
[null,"   • Sprinklered status is a categorical variable with two levels: sprinklered and "]
[null,"      non-sprinklered."]
[null,"   • The natural log of AOI, ln(AOI), is a continuous variable."]
[null,"   • The log link function is selected."]
[null,"   • An interaction variable is included as ln(AOI) for sprinklered and zero otherwise."]
[null,"   • The model results are as follows:"]
[null,null,"Parameter",null,"Coefficient"]
[null,null,"Intercept",null,-8.4606999999999992]
[null,null,"Occupancy Class 2",null,0.27139999999999997]
[null,null,"Occupancy Class 3",null,0.36199999999999999]
[null,null,"Occupancy Class 4",null,3.95E-2]
[null,null,"Sprinklered",null,0.7228]
[null,null,"ln(AOI)",null,0.43109999999999998]
[null,null,"Sprinklered: Yes, ln(AOI)",null,-9.6000000000000002E-2]
[]
["(a)","Calculate the ratio of the estimated model frequency of a sprinklered property to that of a"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A22,'Point Grid'!$C$7:$I$7,0))","v":0.75},"non-sprinklered property for AOI = 200,000 and Occupancy Class 2."]
[]
[]
["(b)","Calculate the intercept term if AOI is centered at the base level of 200,000."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A26,'Point Grid'!$C$7:$I$7,0))","v":0.75}]
[]
[]
["(c)","Briefly describe two advantages of centering variables of a GLM at their base levels."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A30,'Point Grid'!$C$7:$I$7,0))","v":0.5}]

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[7,"Incomplete",null,null,null,"Formula Sheet",null,null,null,null,"Navigator",null,null,"Solution"]
[]
["Points","An actuary is pricing a workers compensation policy. Given the following:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('7'!A1,'Point Grid'!A:A,0))","v":7.5},null,"Policy Effective Date",null,null,null,"2020-01-01"]
[null,null,"Policy Term",null,null,null,"One year"]
[null,null,"Annual Loss Trend",null,null,null,4.4999999999999998E-2]
[null,null,"Cap for individual claims",null,null,null,100000]
[null,null,"Credibility factor",null,null,null,0.4]
[null,null,"Expected ultimate loss before modification",null,null,null,1064000]
[]
[null,"As of June 30, 2019, ground up reported losses are:"]
[null,null,"Policy Year","Total Reported Loss",null,"Individual Claims over $100,000"]
[null,null,2016,392457,null,128305]
[null,null,2017,1013863,null,525626,152860]
[null,null,2018,459798,null,275865]
[null,null,2019,181325,null,"None"]
[]
[null,"The following limited loss development factors (LDFs) apply to this policy:"]
[null,null,"Maturity to Ultimate","Limited LDF"]
[null,null,"42 months",1.052]
[null,null,"30 months",1.0940000000000001]
[null,null,"18 months",1.286]
[]
[null,"Based on an internal study, the actuary believes that claim severity follows a shifted Pareto distribution"]
[null,"with α = 1.3 and β = 22,800."]
[]
[null,"The following expenses apply to this policy:"]
[null,null,"Loss Adjustment Expense (LAE)",null,"7.5% of loss"]
[null,null,"Taxes and Fees",null,"3.5% of gross premium"]
[null,null,"Acquisition",null,"17% of gross premium"]
[null,null,"Profit and Contingencies",null,"0% of gross premium"]
[]
[null,"The insurer's management is concerned about capacity on risks of this type. To address these concerns,"]
[null,"they are requiring facultative reinsurance to support this account. Under the treaty, the reinsurer would"]
[null,"assume all aggregate losses between $2,000,000 and $4,000,000. The primary insurer will retain all LAE."]
[]
[null,"The primary insurer's actuary believes the following Table M and the associated expected loss groupings"]
[null,"(ELGs) are appropriate for risks of this type:"]
[]
[null,"ELG","Loss Range",null,null,null,null,"ELG"]
[null,31,"$730,000 – 820,000",null,"Entry Ratio",31,30,29,28,27,26]
[null,30,"$820,001 – 930,000",null,1.5,0.18759999999999999,0.1764,0.16489999999999999,0.15290000000000001,0.14419999999999999,0.1343]
[null,29,"$930,001 – 1,090,000",null,1.75,0.14899999999999999,0.1376,0.12570000000000001,0.11310000000000001,0.1048,9.6299999999999997E-2]
[null,28,"$1,090,001 – 1,280,000",null,2,0.1195,0.10829999999999999,9.64E-2,8.3799999999999999E-2,7.6200000000000004E-2,6.9199999999999998E-2]
[null,27,"$1,280,001 – 1,515,000",null,2.25,9.6799999999999997E-2,8.5900000000000004E-2,7.4499999999999997E-2,6.2300000000000001E-2,5.5500000000000001E-2,4.9700000000000001E-2]
[null,26,"$1,515,001 – 1,844,000",null,2.5,7.9100000000000004E-2,6.8699999999999997E-2,5.79E-2,4.65E-2,4.0399999999999998E-2,3.5700000000000003E-2]
[null,null,null,null,2.75,6.5199999999999994E-2,5.5399999999999998E-2,4.53E-2,3.4700000000000002E-2,2.9499999999999998E-2,2.5700000000000001E-2]
[null,null,null,null,3,5.4100000000000002E-2,4.4999999999999998E-2,3.56E-2,2.5999999999999999E-2,2.1499999999999998E-2,1.8499999999999999E-2]
[null,null,null,null,3.25,4.5199999999999997E-2,3.6700000000000003E-2,2.8199999999999999E-2,1.9599999999999999E-2,1.5699999999999999E-2,1.3299999999999999E-2]
[null,null,null,null,3.5,3.7999999999999999E-2,3.0200000000000001E-2,2.24E-2,1.4800000000000001E-2,1.15E-2,9.5999999999999992E-3]
[null,null,null,null,3.75,3.2099999999999997E-2,2.5000000000000001E-2,1.7899999999999999E-2,1.11E-2,8.3999999999999995E-3,6.8999999999999999E-3]
[null,null,null,null,4,2.7300000000000001E-2,2.07E-2,1.44E-2,8.3999999999999995E-3,6.1999999999999998E-3,5.0000000000000001E-3]
[]
["(a)","Calculate the expected ground up reported loss limited to $100,000 per claim for this insured for the three"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A54,'Point Grid'!$C$7:$I$7,0))","v":2.25},"years of experience combined."]
[]
[]
["(b)","Calculate the total modified ground up unlimited expected loss for this policy."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A58,'Point Grid'!$C$7:$I$7,0))","v":1.5}]
[]
[]
["(c)","Alternatively, the actuary could have trended and developed reported losses to the cost level of the "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A62,'Point Grid'!$C$7:$I$7,0))","v":0.25},"prospective policy period. Briefly explain why this approach would not produce an identical modification"]
[null,"factor."]
[]
["(d)","Calculate the guaranteed cost premium for this insured."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A66,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(e)","Calculate the loss expected to be ceded to the reinsurer under this treaty. Round to the nearest entry ratio"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A70,'Point Grid'!$C$7:$I$7,0))","v":1.5},"(i.e. do not interpolate)."]
[]
[]
["(f)","A reinsurer has quoted a premium of $200,000 for this treaty. Calculate the premium the primary insurer must charge in "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A74,'Point Grid'!$C$7:$I$7,0))","v":1},"order to maintain the same underwriting profit."]
[]
[]
["(g)","Explain how the assumptions of the primary insurer's actuary may have resulted in an inequitable premium calculated in"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A78,'Point Grid'!$C$7:$I$7,0))","v":0.5},"part (f) above."]

{"sheet":"8","index":11,"n_rows":19,"n_cols":9,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
[8,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","Given the following for a policy:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('8'!A1,'Point Grid'!A:A,0))","v":1.5},"   • Basic Limit = 100,000"]
[null,"   • Expected Basic Limit Indemnity = 65,000"]
[null,"   • Allocated Loss Adjustment Expense (ALAE) = 20% of Indemnity"]
[null,"   • Unallocated Loss Adjustment Expense = 1.5% of Indemnity and ALAE"]
[null,"   • All other expenses are variable and are 15% of the premium"]
[null,"   • Risk load = 0%"]
[null,"   • Profit load = 2.5%"]
[null,"   • The following table shows Indemnity-only limited expected severity:"]
[null,null,"Limit","E[X; L]"]
[null,null,100000,58750]
[null,null,200000,100000]
[null,null,500000,156250]
[null,null,1000000,218750]
[]
["(a)","Calculate the premium for this policy with a 500,000 limit over a 500,000 deductible."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A18,'Point Grid'!$C$7:$I$7,0))","v":1.5}]

{"sheet":"9","index":12,"n_rows":15,"n_cols":9,"rows_kept":15,"cut":false,"hidden":false,"merged":[[8,3,9,3],[8,4,9,4],[10,3,11,3],[10,4,11,4],[8,1,9,2],[10,1,11,2]]}
[9,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","An insurer's risk classification system contains four classes (A, B, C, and D). The insurer is considering"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('9'!A1,'Point Grid'!A:A,0))","v":1},"using experience rating to rate all four classes."]
[null,"Given the following:"]
[null,null,null,"Low Variance of","High Variance of"]
[null,null,null,"Hypothetical Means","Hypothetical Means"]
[null,null,null,"within Class","within Class"]
[null,"Low Expected Value of \nProcess Variance",null,"Class A","Class B"]
[]
[null,"High Expected Value of\nProcess Variance",null,"Class C","Class D"]
[]
[]
["(a)","From the insurer's perspective, briefly explain the class for which experience rating is expected to be"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A14,'Point Grid'!$C$7:$I$7,0))","v":1},"the most useful and the class for which experience rating is expected to be the least useful."]

{"sheet":"10","index":13,"n_rows":50,"n_cols":9,"rows_kept":50,"cut":false,"hidden":false,"merged":[]}
[10,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","An actuary has created new models to calculate the experience modification factor for two lines of"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('10'!A1,'Point Grid'!A:A,0))","v":1.5},"business. Given the following:"]
[null,"   • Line of business 1 (currently does not use experience rating)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"   • Line of business 2 (currently uses experience rating)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,"Line of Business 2","Efficiency Test"]
[null,null,"Current Plan",3.4599999999999999E-2]
[null,null,"Proposed Plan",0.11840000000000001]
[]
[null,"For both lines of business, assume that the cost of implementation is negligible."]
[]
["(a)","For line of business 1, evaluate whether the new experience modification should be implemented."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A41,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(b)","For line of business 1, describe a way to improve the results of the experience modification."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A45,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(c)","For line of business 2, evaluate whether the proposed plan should be used."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A49,'Point Grid'!$C$7:$I$7,0))","v":0.5}]

{"sheet":"11","index":14,"n_rows":37,"n_cols":9,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
[11,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","Consider the following sample of five insurance risks which have been experience rated:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('11'!A1,'Point Grid'!A:A,0))","v":3.75},"Risk","Mod","Manual Loss Ratio","Standard Loss Ratio"]
[null,1,0.6,0.6,1]
[null,2,0.79,0.8,1.01]
[null,3,"X",0.96,"Y"]
[null,4,1.1000000000000001,1.1000000000000001,1]
[null,5,1.1399999999999999,1.1499999999999999,1.01]
[]
[null,"The actual claims for Risk 3 in the experience period are as follows:"]
[null,null,"Claim #","Incurred Loss Amount"]
[null,null,"001",3200]
[null,null,"002",3000]
[null,null,"003",2800]
[null,null,"004",2700]
[null,null,"005",3300]
[null,null,"006",2900]
[null,null,"007",10000]
[null,null,"008",3100]
[null,null,"009",3000]
[null,null,"010",3100]
[null,null,"Total",{"$f":"SUM(D13:D22)","v":37100}]
[]
[null,"• Expected Losses for Risk 3 in the experience period = 32,000"]
[null,"• Credibility factor = 0.75"]
[]
["(a)","Calculate the modification factor, X, for Risk 3."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A28,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(b)","Provide a recommendation to improve the effectiveness of experience rating for Risk 3 and "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A32,'Point Grid'!$C$7:$I$7,0))","v":0.5},"briefly justify."]
[]
[]
["(c)","Show, quantitatively, that the recommendation in part (b) above improves the plan. "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A36,'Point Grid'!$C$7:$I$7,0))","v":2.75},"Assume no other risks are impacted by the recommendation."]

{"sheet":"12","index":15,"n_rows":46,"n_cols":9,"rows_kept":46,"cut":false,"hidden":false,"merged":[]}
[12,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","An actuary is assessing the current Table M underlying the pricing of a book of business. All policies"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('12'!A1,'Point Grid'!A:A,0))","v":2},"within the book of business have identical expected losses and are expected to have exactly one"]
[null,"claim during the policy period. The actuary divides the book of business into two subsets of "]
[null,"policies, Subset A and Subset B, and finds the following distributions of aggregate losses:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["(a)","Discuss why the current Table M may not be appropriate for this book of business."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A35,'Point Grid'!$C$7:$I$7,0))","v":0.5}]
[]
[]
["(b)","Using the observations in Subset B, calculate the insurance charges associated with the following"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A39,'Point Grid'!$C$7:$I$7,0))","v":1},"claim sizes:"]
[null,"   i. 10,000"]
[null,"  ii. 40,000"]
[null," iii. 80,000"]
[]
["(c)","Briefly describe two considerations when using the Table M calculated in part (b) above to support"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A45,'Point Grid'!$C$7:$I$7,0))","v":0.5},"the creation of a Table M for a different line of insurance."]

{"sheet":"13","index":16,"n_rows":22,"n_cols":9,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[13,"Incomplete",null,"Formula Sheet",null,null,"Navigator",null,"Solution"]
[]
["Points","For a given policy that provides first dollar coverage, there is a 50% probability that no claims will"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('13'!A1,'Point Grid'!A:A,0))","v":2},"occur during the policy period. Given that a claim does occur, the frequency distribution is shown"]
[null,"below:"]
[null,"Number of Claims","Probability"]
[null,1,0.7]
[null,3,0.2]
[null,5,0.1]
[]
[null,"The claim-size variable X for this policy follows a shifted Pareto distribution with the following"]
[null,"characteristics:"]
[null,"   • eX(6,000) = 15,000"]
[null,"   • E[X] = 3,000"]
[null,"   • E[X; 4,000] = 1,433.30"]
[]
["(a)","Calculate the expected aggregate loss in the layer 1,000 excess of 4,000 for this policy."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A17,'Point Grid'!$C$7:$I$7,0))","v":1.5}]
[]
[]
["(b)","Explain one difficulty that can arise when trying to fit an aggregate loss distribution function to"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A21,'Point Grid'!$C$7:$I$7,0))","v":0.5},"losses in an excess layer."]

{"sheet":"14","index":17,"n_rows":22,"n_cols":9,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[14,"Incomplete",null,null,null,null,"Navigator",null,"Solution"]
[]
["Points","An insured is written under a retrospective rating plan with a minimum and a maximum premium"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('14'!A1,'Point Grid'!A:A,0))","v":2},"with the following parameters:"]
[null,"Loss Conversion Factor",1.07]
[null,"Expected Loss",825000]
[null,"Expenses",20000]
[null,"φ(rG)",0.4]
[null,"φ(rH)",0.8]
[null,"rG",1.21]
[null,"rH",0.5]
[]
["(a)","Calculate the basic premium."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A13,'Point Grid'!$C$7:$I$7,0))","v":1}]
[]
[]
["(b)","Upon renewal, the insured requests that a per-occurrence claim limit of $200,000 be added to the "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A17,'Point Grid'!$C$7:$I$7,0))","v":1},"current policy. The pricing actuary estimates that, on average, the insured will have $400,000 of losses"]
[null,"that exceed this per-occurrence limit during the next policy period. To calculate the expected increase"]
[null,"to the basic premium, the actuary loads the $400,000 for expenses and profit."]
[]
[null,"Fully discuss the appropriateness of the actuary's methodology."]

{"sheet":"15","index":18,"n_rows":38,"n_cols":9,"rows_kept":38,"cut":false,"hidden":false,"merged":[[0,5,0,6]]}
[15,"Incomplete",null,"Formula Sheet",null,"Navigator",null,null,"Solution"]
[]
["Points","An actuary is pricing a retrospectively rated policy with a per-occurrence limit of 20,000 and no"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('15'!A1,'Point Grid'!A:A,0))","v":3.5},"minimum or maximum ratable loss."]
[]
[null,"Using claim data from a group of similar policies, the actuary fit the following regression line to the"]
[null,"to the excess severity to estimate losses using the shifted Pareto distribution. The fitted regression"]
[null,"function is y = 0.4467x + 16112 with R2 = 0.9826."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Given the following:",null,null,null,"Included in:"]
[null,"Loss adjustment expenses as a percentage of loss",null,null,0.1,"Loss conversion factor"]
[null,"Commission as a percentage of retrospective premium",null,null,0.09,"Tax multiplier"]
[null,"Premium tax as a percentage of retrospective premium",null,null,0.08,"Tax multiplier"]
[null,"Fixed overhead expenses",null,null,50000,"Basic premium"]
[null,"Underwriting profit as a percentage of expected excess loss",null,null,0.06,"Basic premium"]
[]
[null,"   • The number of claims for ground up losses is Poisson distributed with λ = 15."]
[]
["(a)","Calculate the basic premium."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A29,'Point Grid'!$C$7:$I$7,0))","v":2}]
[]
[]
["(b)","Assuming that actual limited losses equal half the expected limited losses, calculate the "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A33,'Point Grid'!$C$7:$I$7,0))","v":1},"retrospective premium."]
[]
[]
["(c)","Assess the actuary's decision to use the shifted Pareto distribution to estimate excess severity."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A37,'Point Grid'!$C$7:$I$7,0))","v":0.5}]

{"sheet":"16","index":19,"n_rows":31,"n_cols":9,"rows_kept":31,"cut":false,"hidden":false,"merged":[[3,3,5,3],[3,4,5,4],[3,2,5,2],[0,5,0,6]]}
[16,"Incomplete",null,null,null,"Navigator",null,null,"Solution"]
[]
["Points","The loss experience of five similarly sized risks is shown in the table below:"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('16'!A1,'Point Grid'!A:A,0))","v":3},null,"Risk","Aggregate Unlimited Loss","Aggregate Limited Loss"]
[]
[]
[null,null,1,30000,30000]
[null,null,2,95000,60000]
[null,null,3,110000,90000]
[null,null,4,160000,60000]
[null,null,5,415000,360000]
[null,null,"Total",{"$f":"SUM(D7:D11)","v":810000},{"$f":"SUM(E7:E11)","v":600000}]
[null,"Limited losses have a per-occurrence limit of 50,000 applied."]
[]
["(a)","Construct a Limited Loss Table M based on the experience above, displaying entry ratios"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A15,'Point Grid'!$C$7:$I$7,0))","v":1.5},"ranging from 0 to 3 in increments of 0.5 and the corresponding insurance charges."]
[]
[]
["(b)","An insured similar to the risks above is evaluating three potential policies:"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A19,'Point Grid'!$C$7:$I$7,0))","v":1.5},"  1. A guaranteed cost policy"]
[null,"  2. A large dollar deductible policy with a 50,000 per-occurrence limit"]
[null,"  3. A retrospectively rated policy with an underlying 200,000 aggregate limit and no"]
[null,"       per-occurrence limit."]
[]
[null,"Given the following:"]
[null,"   • The insured would like to minimize cost"]
[null,"   • Maintaining a stable, predictable cash flow is a priority for the insured"]
[null,"   • The insured has recently implement a successful claim severity reduction program."]
[]
[null,"Briefly discuss one advantage and one disadvantage of each of the three policies from "]
[null,"the perspective of this insured."]

{"sheet":"17","index":20,"n_rows":23,"n_cols":9,"rows_kept":23,"cut":false,"hidden":false,"merged":[[13,2,15,2],[13,3,15,3],[13,1,15,1],[0,5,0,6]]}
[17,"Incomplete",null,null,null,"Navigator",null,null,"Solution"]
[]
["Points","An insurer is deciding on a proportional reinsurance strategy for the upcoming two years."]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('17'!A1,'Point Grid'!A:A,0))","v":3},"A reinsurer proposed the following sliding-scale commission with a carry-forward "]
[null,"provision. The contract will be identical for the second year."]
[null,"Minimum Commission:",null,"12.5% at an 80% loss ratio"]
[null,"Sliding 1:1 to",null,"27.5% at a 65% loss ratio"]
[null,"Sliding 0.5:1 to a Maximum",null,"35% at a 50% loss ratio"]
[]
[null,"Assume the insurer places no value on the carry-forward provision after the second year, and"]
[null,"ignore the time value of money (i.e., assume a 0% interest rate)."]
[]
[null,"The following table details the expected loss distribution of the underlying business:"]
[null,"Range of Loss Ratios","Average Loss Ratio in Range","Probability of Being in Range"]
[]
[]
[null,"0% – 50%",0.43,0.15]
[null,"50% – 60%",0.56999999999999995,0.25]
[null,"60% – 80%",0.68,0.45]
[null,"80% or above",0.85,0.15]
[]
["(a)","Calculate the reinsurer's expected technical ratio for each year if the insurer buys the "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A22,'Point Grid'!$C$7:$I$7,0))","v":3},"sliding-scale commission contract for both years."]

{"sheet":"18","index":21,"n_rows":58,"n_cols":8,"rows_kept":58,"cut":false,"hidden":false,"merged":[[17,4,19,4],[17,1,19,1],[17,2,19,2],[17,3,19,3]]}
[18,"Incomplete",null,null,null,"Navigator",null,"Solution"]
[]
["Points","A property insurer has an existing Quota Share reinsurance treaty in place. The insurer would"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('18'!A1,'Point Grid'!A:A,0))","v":5.5},"like to further reduce its net loss exposure by exploring a proposed Property Per Risk Excess"]
[null,"reinsurance treaty. Given the following:"]
[null,"Existing Quota Share Reinsurance Treaty"]
[null,"   • 25% Quota Share"]
[null,"   • 15% Ceding Commission"]
[]
[null,"Proposed Property Per Risk Excess Reinsurance Treaty"]
[null,"   • Subject premium of $100 million net of the Quota Share reinsurance treaty"]
[null,"   • Cover net losses in excess of $500,000, up to a limit of $500,000"]
[null,"   • The Quota Share reinsurance treaty will inure to the benefit of this treaty"]
[null,"   • Ceded Loss Ratio for this Excess layer is estimated to be 90%"]
[]
[null,"The table below illustrates the insurer's historical experience data net of the Quota Share that"]
[null,"is subject to the proposed Property Per Risk Excess layer:"]
[null,"Historical Accident Year","On Level Subject Earned Premium ($ millions)","On Level Trended Ultimate Subject Loss Ratio","On Level Trended Ultimate Layer Loss Cost"]
[]
[]
[null,2014,100,0.75,0.25]
[null,2015,120,0.75,0.3]
[null,2016,150,0.9,0.45]
[null,2017,80,0.75,0.24]
[null,2018,100,0.8,0.36]
[]
["(a)","Calculate the loss cost of the Property Per Risk Excess layer using all 5 years of historical"]
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[]
[]
["(b)","Assume that the following exposure curve definition applies to the Property Per Risk Excess"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A31,'Point Grid'!$C$7:$I$7,0))","v":1},"layer:"]
[]
[null,"where G(x) represents the ratio of pure risk premiums retained by the insurer, and x represents"]
[null,"the ground up loss normalized to the maximum possible loss of $1 million."]
[]
[null,"Calculate the loss cost of the Property Per Risk Excess layer retained by the reinsurer based on"]
[null,"the exposure curve."]
[]
["(c)","Calculate the loss cost of the Property Per Risk Excess layer using a blend of the experience"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A40,'Point Grid'!$C$7:$I$7,0))","v":0.5},"loss cost and the exposure loss cost based on a credibility weight of 80%."]
[]
[]
["(d)","The insurer's historical gross expenses are estimated to be 15% of historical gross premiums."]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A44,'Point Grid'!$C$7:$I$7,0))","v":2},"Calculate the insurer's expected net underwriting profit after application of both the existing"]
[null,"Quota Share reinsurance treaty and the proposed Property Per Risk Excess reinsurance treaty."]
[]
[null,"The insurer is also exploring the following proposed modifications to the Quota Share"]
[null,"reinsurance treaty:"]
[null,"   • Option 1: Profit Commission equal to 100% of reinsurer profit above a 5% reinsurer margin"]
[null,"   • Option 2: 20% Ceding Commission"]
[]
["(e)","Calculate the 5-year weighted average ratio of profit commission to ceded premium for the "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A53,'Point Grid'!$C$7:$I$7,0))","v":1},"Quota Share reinsurance treaty using the historical experience data provided."]
[]
[]
["(f)","Briefly describe one advantage and one disadvantage of implementing the proposed profit"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A57,'Point Grid'!$C$7:$I$7,0))","v":0.5},"commission versus the higher ceding commission from the insurer's perspective."]

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[19,"Incomplete",null,null,null,"Navigator",null,null,"Solution"]
[]
["Points","An insurance company is deciding between three reinsurance treaty options from the same"]
[{"$f":"INDEX('Point Grid'!B:B,MATCH('19'!A1,'Point Grid'!A:A,0))","v":1.75},"reinsurance company based on the following output from a catastrophe model:"]
[]
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[]
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[]
[]
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[null,"Insurance Company","Gross","Option 1","Option 2","Option 3"]
[null,null,"(No Reinsurance)"]
[null,"Retained AAL","$500 million","$450 million","$486 million","$488 million"]
[null,"Coefficient of Variation of Retained Loss",0.25,0.25,0.24,0.22]
[]
[null,"Coefficient of Variation of Ceded Loss","N/A",0.25,0.76,1.69]
[]
[]
["(a)","Calculate the probability that the insurance company retains more than $750 million of loss on"]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A38,'Point Grid'!$C$7:$I$7,0))","v":0.5},"a gross basis."]
[]
[]
["(b)","One of the options represents a Quota Share reinsurance treaty. Justify which of the three options "]
[{"$f":"INDEX('Point Grid'!$C$8:$I$26,MATCH($A$1,'Point Grid'!$A$8:$A$26,0),MATCH(A42,'Point Grid'!$C$7:$I$7,0))","v":0.75},"it is, and state the Quota Share percentage."]
[]
[]
["(c)","Describe a reason why the reinsurance premium for Option 3 may be higher compared to Option 1."]
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