S. BROVERMAN EXAM MLC STUDY GUIDE - VOLUME 1 - ACTEX / Mad River

TABLE OF CONTENTS

S. BROVERMAN EXAM MLC STUDY GUIDE - VOLUME 1

LIFE CONTINGENCIES NOTES, EXAMPLES AND PROBLEM SETS

Introductory Note

TABLE OF CONTENTS - PART A

Section 1 - Review of Preliminary Topics Problem Set 1 - Review of Preliminary Topics - Section 1 Section 2 - Models for Survival and Mortality Section 3 - The Force of Mortality Section 4 - The Life Table Section 5 - Mean and Variance of XB and OB Section 6 - Parametric Survival Models Section 7 - Fractional Age Assumptions Section 8 - Select and Ultimate Mortality Problem Set 2 - Survival and Mortality - Sections 2 to 8 Section 9 - One-Year Term Insurance Payable at the End of the Year of Death Section 10 - Term and Whole Life Insurance

Payable at the End of the Year of Death Section 11 - Pure Endowment and Other Life Insurances

Payable at the End of the Year of Death Section 12 - Insurance Payable at the Moment of Death Section 13 - Additional Insurance Relationships Problem Set 3 - Life Insurance - Sections 9 to 13 Section 14 - Discrete Whole Life Annuity-Due Section 15 - Discrete Life Annuities Section 16 - Continuous Life Annuities Section 17 - Additional Annuity Relationships Problem Set 4 - Life Annuities - Sections 14 to 17 Section 18 - The Loss at Issue Random Variable and

Principles of Premium Calculation Section 19 - Equivalence Principle Premiums Section 20 - Policy Expenses Problem Set 5 - Annual Premiums - Sections 18 to 20

1 to 14 15 to 24 25 to 32 33 to 40 41 to 46 47 to 56 57 to 62 63 to 68 69 to 76 77 to 104 105 to 110

111 to 118

119 to 128 129 to 142 143 to 158 159 to 192 193 to 198 199 to 210 211 to 220 221 to 228 229 to 256

257 to 266 267 to 280 281 to 286 287 to 318

SOA Exam MLC Study Guide ? S. Broverman, 2015



TABLE OF CONTENTS

TABLE OF CONTENTS - PART B

Section 21 - Introduction to Net Reserves Section 22 - Prospective Form of Net Reserves Section 23 - Additional Reserve Representations Section 24 - Reserves on Additional Policy Types Section 25 - Expense-Augmented Reserves Section 26 - Recursion Relationships for Reserves Section 27 - Modified Reserves, Policy Profit Problem Set 6 - Reserves - Sections 21 to 27 Section 28 - The Joint Life Status Section 29 - The Last-Survivor Status and the Common Shock Model Section 30 - Multiple Life Insurances and Annuities Section 31 - Contingent Probabilities and Insurances Problem Set 7 - Multiple Life - Sections 28 to 31 Section 32 - Multiple Decrement Models Section 33 - Associated Single Decrement Tables Section 34 - Valuation of Multiple Decrement Benefits , Asset Shares,

Non-Forfeiture Values and Policy Profit Analysis Section 35 - Pension Mathematics Problem Set 8 - Multiple Decrement Models - Sections 32 to 35 Section 36 - Discrete Time Markov Chains - One-Step Transitions Section 37 - Discrete Time Markov Chains - Multi-Step Transitions Section 38 - Continuous Time Markov Chains Section 39 - Continuous Time Markov Chain Models Problem Set 9 - Markov Chains -Sections 36 to 39 Section 40 - Term Structure, Yield Curves and Risk Problem Set 10 - Variable Interest Rates - Section 40 Section 41 - Profit Testing an Insurance Policy Section 42 - Participating Insurance and Universal Life Insurance Problem Set 11 - Profit Testing, Participating

and Universal Life Insurance - Sections 41 and 41

ILLUSTRATIVE LIFE TABLE

319 to 324 325 to 330 331 to 340 341 to 346 347 to 356 357 to 368 369 to 380 381 to 3408 409 to 416 417 to 424 425 to 436 437 to 444 445 to 468 469 to 480 481 to 494

495 to 500 501 to 504 505 to 536 537 to 544 545 to 550 551 to 560 561 to 568 569 to 582 583 to 592 593 to 602 603 to 610 611 to 618

593 to 602



SOA Exam MLC Study Guide ? S. Broverman, 2015

INTRODUCTORY NOTE

INTRODUCTORY NOTE

This study guide is designed to help in the preparation for Exam MLC of the Society of Actuaries.

The study guide is divided into two volumes. Volume 1 consists of review notes, examples and problem sets. Volume 2 contains 4 practice exams of 20 multiple choice questions each and written questions with a total point value of 56 points. Volume 2 also has 15 multiple choice tests of 20 questions each. In Volume 1, there are close to 200 examples in the notes, over 375 multiple choice problems and almost 30 written answer problems in the problem sets. All of these (about 1000) questions have detailed solutions. The notes are broken up into 42 sections Each section has a suggested approximate time frame.

Many of the examples in the notes and about half of the problems in the problem sets are from older SOA or CAS exams on the relevant topics. Some of the questions on the practice exams are variations on actual exam questions. The SOA has posted on its website a sample question file for Exam MLC with solutions. Many of those questions are from old exams, and there may be some overlap in the questions found in this study guide and those found in the SOA files, but I have attempted to limit that duplication. The SOA and CAS questions are copyrighted by the SOA and CAS, and I gratefully acknowledge that I have been permitted to include them in this study guide.

Because of the time constraint on the exam, a crucial aspect of exam taking is the ability to work quickly. I believe that working through many problems and examples is a good way to build up the speed at which you work. It can also be worthwhile to work through problems that have been done before, as this helps to reinforce familiarity, understanding and confidence. Working many problems will also help in being able to more quickly identify topic and question types. I have attempted, wherever possible, to emphasize shortcuts and efficient and systematic ways of setting up solutions. There are also occasional comments on interpretation of the language used in some exam questions. While the focus of the study guide is on exam preparation, from time to time there will be comments on underlying theory in places that I feel those comments may provide useful insight into a topic.

It has been my intention to make this study guide self-contained and comprehensive for all Exam MLC topics, but there are may be occasional references to the book listed in the SOA exam catalog. While the ability to derive formulas used on the exam is usually not the focus of an exam question, it is useful in enhancing the understanding of the material and may be helpful in memorizing formulas. There may be an occasional reference in the review notes to a derivation, but you are encouraged to review the official reference material for more detail on formula derivations.

In order for the review notes in this study guide to be most effective, you should have some background at the junior or senior college level in probability and statistics. It will be assumed that you are reasonably familiar with differential and integral calculus.

SOA Exam MLC Study Guide ? S. Broverman, 2015



INTRODUCTORY NOTE

Of the various calculators that are allowed for use on the exam, I think that the BA II PLUS is probably the best choice. It has several memories and has good financial functions. I think that the TI-30X IIS would be the second best choice.

There is a set of tables that has been provided with the exam in past sittings. These tables consist of a standard normal distribution probability table and a life table with insurance and annuity values at a 6% rate of interest. The tables are available for download from the Society of Actuaries website, but are included at the ends of both Volumes 1 and 2 for convenience.

If you have any questions, comments, criticisms or compliments regarding this study guide, you may contact me at the address below. I apologize in advance for any errors, typographical or otherwise, that you might find, and it would be greatly appreciated if you would bring them to my attention. I will be maintaining a website for errata that can be accessed from . It is my sincere hope that you find this study guide helpful and useful in your preparation for the exam. I wish you the best of luck on the exam.

Samuel A. Broverman Department of Statistics University of Toronto 100 St. George Street Toronto, Ontario CANADA M5S 3G3 E-mail: sam@utstat.toronto.edu or 2brove@ Internet:

January, 2015



SOA Exam MLC Study Guide ? S. Broverman, 2015

MLCS SECTION 14 - DISCRETE WHOLE-LIFE ANNUITY-DUE

MLC SECTION 14 - DISCRETE WHOLE LIFE ANNUITY-DUE

The suggested time frame for covering this section is 2 hours.

A life annuity is an ongoing series of payments made while someone remains alive. A life

annuity-due is an annuity with annual payments paid at the start of each year and payable over

some period related to an individual's lifetime. In the formulations that follow, we will make use

of the compound interest annuity-due,

?+?7l

oe " @ @# ? @7"

oe

"@7 "@

oe

"@7 .

,

where . is the annual effective rate of discount.

Whole Life Annuity-Due of 1 Per Year

We can describe the actuarial present value of a life annuity-due by considering the present value of the "average" amount an insurer will have to pay. Suppose an insurer issues a life annuity-due of 1 per year to jB individuals. Based on the expected numbers of survivors from year to year, the amount that the insurer expects to pay can be described by the following time diagram.

Age/time B?!

l Insurer pays 1 to each of jB

B "?"

B #?#

l

l

?

jB"

jB#

?

B 5?5

l

?

jB5

?

The present value of the total expected payment by the insurer is jB @jB" @#jB# ? @5jB5 ? oe @5 jB5 .

5oe!

The present value per individual annuity is

?

" jB

??jB

@jB"

@#jB#

?

@5 jB5

??

oe

5oe!

@5

jB5 jB

oe @5 5:B.

5oe!

This is the actuarial present value of the whole life annuity-due, and it is denoted ?+?B.

The formulation ?+?B oe @5 5:B may be referred to as the current payment form of the

5oe!

annuity. This life annuity is a sum of a series of pure endowments, one for each integer year.

The Exam MLC Illustrative Life Table provides a column of whole-life annuity-due values at

integer ages.

SOA Exam MLC Study Guide ? S. Broverman, 2015

193

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download