"SOA Exam MLC & CAS Exam 3L Study Supplement," Midwestern

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Transcript of "SOA Exam MLC & CAS Exam 3L Study Supplement," Midwestern

  • SOA EXAM MLC & CAS EXAM 3L STUDY

    SUPPLEMENT

    by Paul H. Johnson, Jr., PhD.

    Last Modified: October 2012

    A document prepared by the author as study materials for theMidwestern Actuarial Forums Exam Preparation Seminars

    This document is not to be redistributed or reproduced in any formwithout permission from the author.

    This document is not in any way officially affiliated withthe Society of Actuaries or the Casualty Actuarial Society.

  • i

    Contents

    PREFACE iv

    AUTHOR BACKGROUND vi

    1 SURVIVAL MODELS AND LIFE TABLES 11.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 23

    2 SELECTION (Exam MLC Only) 242.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 30

    3 INSURANCE BENEFITS I 313.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 57

    4 INSURANCE BENEFITS II (Exam MLC Only) 584.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 71

    5 ANNUITIES I 725.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 725.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 91

    6 ANNUITIES II (Exam MLC Only) 926.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 926.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 107

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    7 PREMIUM CALCULATION I 1087.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 124

    8 PREMIUMCALCULATION II (ExamMLC Only)1258.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 1258.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1308.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 138

    9 RESERVES I 1399.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 1399.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1509.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 158

    10 RESERVES II (Exam MLC Only) 15910.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 15910.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17310.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 182

    11 MULTIPLE STATE MODELS (Exam MLC Only)18311.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 18311.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18811.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 193

    12 MULTIPLE DECREMENTS I 19412.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 19412.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19812.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 204

    13 MULTIPLE DECREMENTS II (ExamMLC Only)20513.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 20513.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21413.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 222

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    14 MULTIPLE LIVES I 22314.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 22314.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23314.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 240

    15 MULTIPLE LIVES II (Exam MLC) 24115.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 24115.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24815.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 253

    16 OTHER TOPICS (Exam MLC Only) 25416.1 Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 25416.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26316.3 Past Exam Questions . . . . . . . . . . . . . . . . . . . . . 275

    17 REFERENCES 276

    18 APPENDIX 27718.1 APPENDIX A: EXAM SYLLABI, EXAM TABLES,

    AND PAST EXAM QUESTIONS . . . . . . . . . . . . . 27718.2 APPENDIX B: STANDARD SELECT SURVIVALMODEL

    ANDMULTI-STATEMODEL EXAMPLES (ExamMLCOnly) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

  • iv

    PREFACE

    This study supplement is intended to be an aid to candidates studying foreither Exam MLC (Models for Life Contingencies) of the Society of Actuariesor Exam 3L (Life Contingencies and Statistics) of the Casualty ActuarialSociety. Each section of this study supplement contains key life contingenciesconcepts and major life contingencies formulas with brief interpretations forspecific Exam MLC/3L topics. This study supplement is NOT meant totake the place of an exams required text book or a proper study guide. Forexample, there are no detailed explanations of topics that would be found ina text book and no worked examples of the material that would be found ina study guide.

    For candidates studying for Exam 3L, this study supplement onlycovers the life contingencies material on that exam. That is, this studysupplement does NOT cover any of the statistics material on Exam 3L.

    This study supplement is meant to outline key life contingencies conceptsand major life contingencies formulas associated with Exam MLC or Exam3L, and to provide exercises that are meant to test a candidates basic knowl-edge of the material and to improve the candidates speed in working withcertain concepts and formulas. If the candidate can master the exercises inthis study supplement, the candidate should be in a good position to tackleactual past Exam MLC and/or Exam 3L questions. Many of the exercises inthis study supplement are based on past homework and midterm questionsthat I used in teaching life contingencies classes at the University of Illinoisat Urbana-Champaign. In some cases, the exercise answer choices arerounded. Choose the letter of the answer choice that is closest toyour own answer.

    Once the exercises in this study supplement have been mastered, the candi-date can refer to the listing of past Exam MLC and Exam 3L questions at theend of each section for a more advanced test of the candidates understandingof the material. Web links to past Exam MLC and Exam 3L questions canbe found in Appendix A of this study supplement. Also, some Exam MLCexercises in this study supplement will utilize Multi-State Model Examplesand the Standard Select Survival Model, each from Dickson et al; these

  • v

    figures are provided in Appendix B of this study supplement.

    For candidates enrolled in the Midwestern Actuarial Forums Exam MLC& 3L Seminar, it is expected that each candidate will have read the requiredstudy materials for either Exam MLC or Exam 3L mentioned in the examssyllabus. The candidate is also expected to have read the relevant sectionsof this study supplement and also have worked its relevant exercises PRIORto sitting for the seminar. Furthermore, it is expected that each candidatewill have worked as many of the past Exam MLC and Exam 3L questionsas possible. Exam 3L candidates should attempt problems from the prior 3Lexams first before attempting any problems from prior MLC exams. Also,some sections are marked Exam MLC Only; as you may have guessed,candidates preparing for Exam 3L can skip those sections. I will rely heavilyon candidates asking questions regarding these study supplement exercisesand past Exam MLC and Exam 3L questions DURING the seminar; often,working exercises and past exam questions identifies issues that once resolvedwill enhance the candidates understanding of the material. I would alsocontend that candidates will only get the most out of this seminar if theyhave sufficiently studied for their exam beforehand.

    Candidates should bring a printed or electronic copy of this studysupplement with them to the seminar. Candidates should also printcopies of all tables provided during the exam they will be writing(Exam MLC or Exam 3L) - please refer to Appendix A of this studysupplement. Candidates should also bring copies of any past Exam MLCand/or Exam 3L questions that they wish to discuss during the seminar.

    Despite proofreading, it is possible that this study supplement may containtypos. If there are any questions regarding possible typos, or anything else,please e-mail me at: pjohnson@illinois.edu.

    Best of luck in your exam preparation!

    Regards:

    -Paul H. Johnson, Jr., PhD

  • vi

    AUTHOR BACKGROUND

    Paul H. Johnson, Jr. earned a PhD in Actuarial Science, Risk Managementand Insurance from the University of Wisconsin-Madison in 2008. He iscurrently an Assistant Professor of Actuarial Science in the Department ofMathematics at the University of Illinois at Urbana-Champaign. Paul haspassed all of the preliminary examinations of the Society of Actuaries (themodern day equivalents of Exams P, FM, M, and C). Since 2003, Paul hastaught undergraduate courses meant to prepare students for each the pre-liminary exams of the Society of Actuaries, and has received various honorsand awards for teaching excellence. Most recently, Paul was honored withthe N. Tenney Peck Teaching Award in Mathematics for 2011.