Exam STAM Study Manual
This manual includes GOALCustomizable, versatileonline exam question bank.Thousands of questions!Access your exclusiveStudyPlus bonus content:GOAL Flashcards Formula sheet* Key Code Inside *Exam STAM Study Manual2nd Edition Volumes I, II & IIIAbraham Weishaus, Ph.D., F.S.A., C.F.A., M.A.A.A.NO RETURN IF OPENEDActuarial Study MaterialsLearning Made Easier
TO OUR READERS:Please check A.S.M.’s web site at www.studymanuals.com for errataand updates. If you have any comments or reports of errata, pleasee-mail us at mail@studymanuals.com.ISBN: 978-1-63588-851-5 Copyright 2020 by Actuarial Study Materials (A.S.M.), PO Box 69,Greenland, NH 03840. All rights reserved. Reproduction in whole or in partwithout express written permission from the publisher is strictly prohibited.
ContentsIRatemaking, Severity, Frequency, and Aggregate Loss1Basic Probability1.1 Functions and moments . . . . . . . . . . . . .1.2 Percentiles . . . . . . . . . . . . . . . . . . . . .1.3 Conditional probability and expectation . . . .1.4 Moment and probability generating functions1.5 The empirical distribution . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . .1.3378111213192 Parametric Distributions2.1 Scaling . . . . . . . . . . . . . . . .2.2 Transformations . . . . . . . . . . .2.3 Common parametric distributions2.3.1 Uniform . . . . . . . . . . .2.3.2 Beta . . . . . . . . . . . . . .2.3.3 Exponential . . . . . . . . .2.3.4 Weibull . . . . . . . . . . . .2.3.5 Gamma . . . . . . . . . . .2.3.6 Pareto . . . . . . . . . . . .2.3.7 Single-parameter Pareto . .2.3.8 Lognormal . . . . . . . . . .2.4 The linear exponential family . . .2.5 Limiting distributions . . . . . . .Exercises . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . .292930333334353636373838394244473 Variance3.1 Additivity . . . . . . .3.2 Normal approximation3.3 Bernoulli shortcut . . .Exercises . . . . . . . .Solutions . . . . . . . .5151525354554 Mixtures and Splices4.1 Mixtures . . . . . . . . . . .4.1.1 Discrete mixtures . .4.1.2 Continuous mixtures4.1.3 Frailty models . . . .4.2 Conditional variance . . . .4.3 Splices . . . . . . . . . . . .Exercises . . . . . . . . . . .Solutions . . . . . . . . . . .5959596162636568745 Property/Casualty Insurance Coverages5.1 Automobile insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8585STAM Study Manual—2nd editionCopyright 2019 ASM.iii
ivCONTENTS5.25.35.45.55.1.1 Liability insurance . . . . . . . . . . . . . . . . . . . . . . . . .5.1.2 Uninsured, underinsured, and unidentified motorist coverage5.1.3 Medical benefits . . . . . . . . . . . . . . . . . . . . . . . . . .5.1.4 Collision and other-than-collision coverage . . . . . . . . . . .Homeowners insurance . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.1 Primary dwelling coverage . . . . . . . . . . . . . . . . . . . .5.2.2 Other first-party coverage . . . . . . . . . . . . . . . . . . . . .5.2.3 Liability coverage . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.4 Tenants package . . . . . . . . . . . . . . . . . . . . . . . . . .Workers compensation . . . . . . . . . . . . . . . . . . . . . . . . . . .Business insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Deductibles and policy limits . . . . . . . . . . . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Health Insurance6.1 Major medical insurance . . . . . . . . . .6.1.1 Coverage modifications . . . . . .6.1.2 Variations on major medical . . . .6.1.3 ACA restrictions on health design6.2 Dental insurance . . . . . . . . . . . . . .7.8585868686868888888889899091.939393949596Loss Reserving: Basic Methods7.1 Case reserves and IBNR reserves . . . . . . . . . . . . . . . . .7.2 Three methods for calculating IBNR reserves . . . . . . . . . .7.2.1 Expected loss ratio method . . . . . . . . . . . . . . . .7.2.2 The chain-ladder or loss development triangle method7.2.3 The Bornhuetter-Ferguson method . . . . . . . . . . . .7.2.4 Variance of forecasted losses . . . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9797989999102103103109.8 Loss Reserving: Other Methods8.1 Projecting frequency and severity separately8.2 Closure method . . . . . . . . . . . . . . . . .8.3 Discounted loss reserves . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . .1171171181211231279 Ratemaking: Preliminary Calculations9.1 Basic concepts of ratemaking . . . . . .9.2 Preliminary calculations for ratemaking9.2.1 Loss development and trend . .9.2.2 Expenses . . . . . . . . . . . . . .9.2.3 Credibility . . . . . . . . . . . . .9.2.4 Premium at current rates . . . .Exercises . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . .13313313413413513513613814110 Ratemaking: Rate Changes and Individual Risk Rating Plans10.1 Rate Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.1.1 Calculating the overall average rate change . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.1.2 Updating class differentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145145145147STAM Study Manual—2nd editionCopyright 2019 ASM.
vCONTENTS10.1.3 Balancing back . . .10.2 Individual risk rating plansExercises . . . . . . . . . . .Solutions . . . . . . . . . . .15015115215711 Policy LimitsExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16316817312 Deductibles12.1 Ordinary and franchise deductibles . .12.2 Payment per loss with deductible . . .12.3 Payment per payment with deductibleExercises . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . .18118118118318719913 Loss Elimination RatioExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20720821414 Increased Limits Factors and Indicated Deductible Relativities14.1 Increased limits factors . . . . . . . . . . . . . . . . . . . . .14.2 Indicated deductible relativities . . . . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22322322622823115 ReinsuranceExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23723924016 Risk Measures and Tail Weight16.1 Coherent risk measures . .16.2 Value-at-Risk (VaR) . . . . .16.3 Tail-Value-at-Risk (TVaR) . .16.4 Tail weight . . . . . . . . . .16.5 Extreme value distributionsExercises . . . . . . . . . . .Solutions . . . . . . . . . . .24324324524725225425625817 Other Topics in Severity Coverage ModificationsExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26526827418 BonusesExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28528628819 Discrete Distributions19.1 The (a, b, 0) class .19.2 The (a, b, 1) class .Exercises . . . . .Solutions . . . . .29329329730030520 Poisson/GammaSTAM Study Manual—2nd editionCopyright 2019 ASM.315
viCONTENTSExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31632021 Frequency— Exposure & Coverage Modifications21.1 Exposure modifications . . . . . . . . . . . .21.2 Coverage modifications . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . .32532532532833222 Aggregate Loss Models: Compound Variance22.1 Introduction . . . . . . . . . . . . . . . . .22.2 Compound variance . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . .33733733834235123 Aggregate Loss Models: Approximating DistributionExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36136437124 Aggregate Losses: Severity ModificationsExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38138238925 Aggregate Loss Models: The Recursive FormulaExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39940340626 Aggregate Losses—Aggregate DeductibleExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41341842427 Aggregate Losses: Miscellaneous Topics27.1 Exact Calculation of Aggregate Loss Distribution27.1.1 Normal distribution . . . . . . . . . . . .27.1.2 Exponential and gamma distributions . .27.1.3 Compound Poisson models . . . . . . . .27.2 Discretizing . . . . . . . . . . . . . . . . . . . . .27.2.1 Method of rounding . . . . . . . . . . . .27.2.2 Method of local moment matching . . . .Exercises . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . .43343343343443643743743743944128 Supplementary Questions: Ratemaking, Severity, Frequency, and Aggregate LossSolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .447450II.Parametric Models29 Maximum Likelihood Estimators29.1 Defining the likelihood . . . .29.1.1 Individual data . . . .29.1.2 Grouped data . . . . .29.1.3 Censoring . . . . . . .29.1.4 Truncation . . . . . . .STAM Study Manual—2nd editionCopyright 2019 ASM457.459460460461462463
viiCONTENTS29.1.5 Combination of censoring and truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 Maximum Likelihood Estimators—Special Techniques30.1 Cases when MLE sample mean . . . . . . . . . . .30.1.1 Exponential distribution . . . . . . . . . . . .30.2 Parametrization and shifting . . . . . . . . . . . . . .30.2.1 Parametrization . . . . . . . . . . . . . . . . .30.2.2 Shifting . . . . . . . . . . . . . . . . . . . . . .30.3 Transformations . . . . . . . . . . . . . . . . . . . . .30.3.1 Lognormal distribution . . . . . . . . . . . .30.3.2 Inverse exponential distribution . . . . . . .30.3.3 Weibull distribution . . . . . . . . . . . . . .30.4 Special distributions . . . . . . . . . . . . . . . . . .30.4.1 Uniform distribution . . . . . . . . . . . . . .30.4.2 Pareto distribution . . . . . . . . . . . . . . .30.4.3 Beta distribution . . . . . . . . . . . . . . . .30.5 Bernoulli technique . . . . . . . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . 49249249650831 Variance Of Maximum Likelihood Estimators31.1 Information matrix . . . . . . . . . . . . . . . . . . . . . . . . .31.1.1 Calculating variance using the information matrix . . .31.1.2 Asymptotic variance of MLE for common distributions31.1.3 True information and observed information . . . . . .31.2 The delta method . . . . . . . . . . . . . . . . . . . . . . . . . .31.3 Confidence intervals . . . . . . . . . . . . . . . . . . . . . . . .31.3.1 Normal confidence intervals . . . . . . . . . . . . . . .31.3.2 Non-normal confidence intervals . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52352352352753253453653653754055032 Fitting Discrete Distributions32.1 Poisson distribution . . . . . . . . . . . . . . . . . . .32.2 Negative binomial . . . . . . . . . . . . . . . . . . . .32.3 Binomial . . . . . . . . . . . . . . . . . . . . . . . . .32.4 Fitting (a, b, 1) class distributions . . . . . . . . . . .32.5 Adjusting for exposure . . . . . . . . . . . . . . . . .32.6 Choosing between distributions in the (a, b, 0) classExercises . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . .56156156156256256456556657433 Hypothesis Tests:33.1 D(x) plots .33.2 p–p plots . .Exercises . .Solutions . .58358358458559034 Hypothesis Tests: Kolmogorov-Smirnov34.1 Individual data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34.2 Grouped data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .595595600Graphic Comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .STAM Study Manual—2nd editionCopyright 2019 ASM.
viiiCONTENTSExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 Hypothesis Tests: Chi-square35.1 Introduction . . . . . . . . . . . . . . . . .35.2 Definition of chi-square statistic . . . . . .35.3 Degrees of freedom . . . . . . . . . . . . .35.4 Other requirements for the chi-square test35.5 Data from several periods . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . .602607.61561561762062362462664136 Likelihood Ratio Test and Algorithm, Penalized Loglikelihood Tests36.1 Likelihood Ratio Test and Algorithm . . . . . . . . . . . . . . . . .36.2 Schwarz Bayesian Criterion and Akaike Information Criterion . .Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65165165565766237 Supplementary Questions: Parametric ModelsSolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .669671III675.Credibility38 Classical Credibility: Poisson FrequencyExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67768269239 Classical Credibility: Non-Poisson FrequencyExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69970270540 Classical Credibility: Partial CredibilityExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71171271941 Bayesian Methods—Discrete PriorExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72372674042 Bayesian Methods—Continuous Prior42.1 Calculating posterior and predictive distributions42.2 Recognizing the posterior distribution . . . . . . .42.3 Loss functions . . . . . . . . . . . . . . . . . . . . .42.4 Interval estimation . . . . . . . . . . . . . . . . . .42.5 The linear exponential family and conjugate priorsExercises . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . .75975976476476576676777343 Bayesian Credibility: Poisson/GammaExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78979079844 Bayesian Credibility: Normal/Normal803STAM Study Manual—2nd editionCopyright 2019 ASM.
ixCONTENTSExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45 Bayesian Credibility: Bernoulli/Beta45.1 Bernoulli/beta . . . . . . . . . . .45.2 Negative binomial/beta . . . . .Exercises . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . .806808.81381381681782146 Bayesian Credibility: Exponential/Inverse GammaExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82582883247 Bühlmann Credibility: BasicsExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83583984748 Bühlmann Credibility: Discrete PriorExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85586088049 Bühlmann Credibility: Continuous PriorExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90190591650 Bühlmann-Straub CredibilityExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92993093651 Exact CredibilityExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94394595052 Bühlmann As Least Squares Estimate of Bayes52.1 Regression . . . . . . . . . . . . . . . . . . .52.2 Graphic questions . . . . . . . . . . . . . . .52.3 Cov(X i , X j ) . . . . . . . . . . . . . . . . . . .Exercises . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . .95595595795895996353 Empirical Bayes Non-Parametric Methods53.1 Uniform exposures . . . . . . . . . . .53.2 Non-uniform exposures . . . . . . . .Exercises . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . .96997097297998654 Empirical Bayes Semi-Parametric Methods54.1 Poisson model . . . . . . . . . . . . . . . . .54.2 Non-Poisson models . . . . . . . . . . . . .54.3 Which Bühlmann method should be used?Exercises . . . . . . . . . . . . . . . . . . . .Solutions . . . . . . . . . . . . . . . . . . . .9999991002100310051013.55 Supplementary Questions: CredibilitySTAM Study Manual—2nd editionCopyright 2019 ASM.1021
xCONTENTSSolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025IVPractice Exams10311 Practice Exam 110332Practice Exam 210453Practice Exam 310554Practice Exam 410655Practice Exam 510756Practice Exam 610857Practice Exam 710958Practice Exam 811059Practice Exam 9111710 Practice Exam 10112711 Practice Exam 11113712 Practice Exam 121147AppendicesA Solutions to the Practice ExamsSolutions for Practice Exam 1 . .Solutions for Practice Exam 2 . .Solutions for Practice Exam 3 . .Solutions for Practice Exam 4 . .Solutions for Practice Exam 5 . .Solutions for Practice Exam 6 . .Solutions for Practice Exam 7 . .Solutions for Practice Exam 8 . .Solutions for Practice Exam 9 . .Solutions for Practice Exam 10 . .Solutions for Practice Exam 11 . .Solutions for Practice Exam 12 . 12721282B Solutions to Old ExamsB.1 Solutions to CAS Exam 3, Spring 2005B.2 Solutions to CAS Exam 3, Fall 2005 . .B.3 Solutions to CAS Exam 3, Spring 2006B.4 Solutions to CAS Exam 3, Fall 2006 . .12951295129813011304C Exam Question IndexSTAM Study Manual—2nd editionCopyright 2019 ASM.1307
Lesson 7Loss Reserving: Basic MethodsReading: Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance 3.1–3.6.4, STAM-24-187.1Case reserves and IBNR reservesClaims on first-party coverages tend to be paid out in a fairly short time. Liability claims, however, can take a longtime to settle. The largest claims can take as much as 10 years to settle. Losses may not even be reported that rapidly.The insurer must hold a reserve for losses that have occurred and that have not been fully paid.A company’s incurred claim expense during a year is the amount the company has paid on the claim plus thechange in reserve over the period. For example, consider a loss with the following history: Reported 11/1/2017 Reserve on 12/31/2017: 15,000 Payment of 4,000 made on 4/15/2018 Reserve on 12/31/2018: 35,000 Payment of 10,000 made on 6/12/2019 Reserve on 12/31/2019: 30,000 Payment of 30,000 made on 10/5/2020 and the claim is closedThen the company’s expense for this loss in 2017 is the reserve set up at the end of the year, 15,000. The expensein 2018 is the 4,000 payment plus the increase in reserve, or 4,000 35,000 15,000 24,000. The expense in 2019is the 10,000 payment plus the increase in reserve, or 10,000 30,000 35,000 5,000. The expense in 2020 is thepayment of 30,000 minus the release of the 30,000 reserve, or 0.The claim adjuster estimates the future payments on a claim and sets
Actuarial Study Materials Learning Made Easier Exam STAM Study Manual 2nd Edition Volumes I, II & III Abraham Weishaus, Ph.D., F.S.A., C.F.A., M.A.A.A. NO RETURN IF .
Solutions to the New STAM Sample Questions Revised July 2019 to Add Questions 327 and 328 2019 Howard C. Mahler For STAM, the SOA revised their file of Sample Questions for Exam C. They deleted questions that are no longer on the syllabus of STAM. They added questions 308 to 326, covering material added to the syllabus.
Malinois-Single B 4 A Waterslager enkeling B 4 A Stam of 4 C Section Timbrados Canaries (current year ringed) Single Pair Stam Groep C Timbrados (ring 2018) Enk - stel C 1 Timbrados Original Stam of 4 A C 1 Timbrado klassiek Stam A Timbrados O
Meesterzanger w.s. Onderwater, Q. waterslager 150 pnt. Kamp. stam w.s. Krien Onderwater waterslager 595 pnt. 2e prijs stam w.s. Krien Onderwater waterslager 590 pnt. 3e prijs stam w.s. Andre Toet waterslager 578 pnt. ere prijs stam w.s. Tinus Teeuwen waterslager 548 pnt. Kamp. ste
STAM-09-18 - 1 - SOCIETY OF ACTUARIES . EXAM STAM SHORT-TERM ACTUARIAL MATHEMATICS . EXAM STAM SAMPLE SOLUTIONS . Questions 1- 307 have been taken from the previous set of Exam C sample questions . Questions no longer relevant to the syllabus have been deleted.Question 308 -326 are based on material newly added.
Exam C Exam STAM - First sitting October 2018 Credit for STAM given to students who pass Exam C by its final June 2018 sitting If you are taking Math 523/524, I recommend taking this last sitting of Exam C in June 2018 Exam MLC Exam LTAM - First sitting October 2018
Past exam papers from June 2019 GRADE 8 1. Afrikaans P2 Exam and Memo 2. Afrikaans P3 Exam 3. Creative Arts - Drama Exam 4. Creative Arts - Visual Arts Exam 5. English P1 Exam 6. English P3 Exam 7. EMS P1 Exam and Memo 8. EMS P2 Exam and Memo 9. Life Orientation Exam 10. Math P1 Exam 11. Social Science P1 Exam and Memo 12.
Questions 1- 307 have been taken from the previous set of Exam C sample questions . Questions no longer relevant to the syllabus have been deleted. Some of the questions in this study note are taken from past examinations. The weight of topics in these sample questions is not representative of the weight of topics on the exam.
Stam 80 EDF herbicide for postemergence weed control in rice is formulated as an 80% active extruded dry flowable formulation. STAM 80 EDF-CA is not a hormone-type herbicide, but kills susceptible weeds by direct contact action. For this reason, thorough
