SOLUTION FOR HOMEWORK 12, ACTS 4306
Welcome to your last homework.
Here you will see some actuarial notions that sometimes used on actuarial Exam 1.
1. Notation: B is benefit.
Given: B = min(Y, 10), fY (y) = 2y 3I(y > 1).
Find: E(B).
Solution: Write,
E(B)
SOLUTION FOR HOMEWORK 11, ACTS 4306
Welcome to your 11th homework. This is a collection of transformation, Central Limit
Theorem (CLT), and other topics.
1. Solution: By definition of Z,
Var(Z) = Var(3X Y .5).
We know that Var(aU + b) = a2 Var(U) for any
HOMEWORK 11, ACTS 4306
For each problem, you need to choose a correct answer among 5 given answers.
1. The profit for a new product is given by Z = 3X Y 5. Let X and Y be independent
random variables with Var(X) = 1 and Var(Y ) = 2. What is the variance o
HOMEWORK 12, ACTS 4306
For each problem, you need to choose a correct answer among 5 given answers.
This homework combines specific topics related to actuarial science and includes losses,
deductables, insurance, etc. You are encouraged to read about thes
Section 1
Effective Rates of Interest and Discount
ACTS 4308
Natalia A. Humphreys
1 / 36
Acknowledgement
This work is based on the material in S. Broverman Study
Guide for SOA Exam FM/CAS Exam 2, 2011 Edition and on
the notes prepared by Professor Ryan Gi
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 6
Section 11: Bond valuation.
Section 12: Bond amortization, callable bonds.
Problem 1
A fiveyear 1,000 par value bond pays 4% coupons semiannually. The bond is priced at 1,122 to yield
an a
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 9
Sections 17, 18: Option Strategies.
Problem 1
The prices of European call and put options with a strike price of $100 expiring at the end of 6 months
are $2.56 and $9.57, respectively. The
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 5
Section 9: Amortization of a loan.
Section 10: The sinking fund method of loan repayment.
Problem 1
Suppose that a $15,000 loan for a new car is to be repaid by level payments at the end of
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 8
Section 15: Introduction to financial derivatives, forward and futures contracts.
Section 16: Introduction to options.
Problem 1
A stock is currently priced at 400. The twoyear forward pri
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 3
Section 5: Annuity valuation at any time point.
Section 6: Annuities with differing interest and payment period.
Problem 1
Frank makes deposits of 200 into an account at the beginning of ea
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 2
Section 3. Force of interest, inflation.
Section 4. Annuityimmediate and annuitydue.
Problem 1
You are given that A(t) = Kt2 + Lt + M , for 0 t 2, and that A(0) = 100, A(1) = 111, and
A(2
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 4
Section 7: Annuities whose payments follow a geometric progression.
Section 8: Annuities whose payments follow an arithmetic progression.
Problem 1
Suppose you buy a perpetuitydue with var
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 7
Section 13: Measures of the rate of return on a fund.
Section 14: The term structure of interest rates, forward rates of interest and duration.
Problem 1
On January 1, an investment account
ACTS 4308
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 1
Section 1. Calculus review and effective rates of interest and discount.
Section 2. Nominal rates of interest and discount.
Problem 1
On September 27, Eric deposits 100 into a savings accou
Principles of Actuarial Models: Financial Economics
ACTS 4302

Fall 2014
Course Syllabus
ISNS 3359  0I1
Department of Geosciences, School of Natural Sciences and Mathematics
The University of Texas at Dallas
Course Information
Course
Course Number/Section
Course Title
Term and Dates
ISNS 3359  0I1
Earthquakes & Volcanoes (On
ACTS 6302
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 2
Lesson 2: Comparing Options
Lesson 3: Binomial Trees  Stock, One Period
Problem 1
You are given:
(i) The price of a stock is 33.
(ii) The stock pays continuous dividends at the annual rate of 0.
ACTS 6302
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 3
Lesson 4: Binomial Trees  General
Lesson 5: Other valuation methods of pricing options.
Problem 1
For a 1year European put option on a stock modeled with a binomial tree:
(i) The tree has 2 per
Lesson 4: Binomial Trees  General
ACTS 4302
Natalia A. Humphreys
1 / 25
Acknowledgement
This work is based on the material in ASM MFE Study manual
for Exam MFE/Exam 3F. Financial Economics (7th Edition),
2009, by Abraham Weishaus.
2 / 25
What we will dis
ACTS 6308
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 7
Section 13: Measures of the rate of return on a fund.
Section 14: The term structure of interest rates, forward rates of interest and duration.
Problem 1
On January 1, an investment account is wo
ACTS 6308
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 6
Section 11: Bond valuation.
Section 12: Bond amortization, callable bonds.
Problem 1
A fiveyear 1,000 par value bond pays 4% coupons semiannually. The bond is priced at 1,122 to yield
an annual
ACTS 6308
Instructor: Yuly Koshevnik
HOMEWORK 2
Section 3. Force of interest, inflation.
Section 4. Annuityimmediate and annuitydue.
Due: September 14, 2016
Sufficient work must be shown to get credit for a correct answer. Partial credit may be given fo
ACTS 6302
Instructor: Yuly Koshevnik
HOMEWORK 1
Lesson 0: Review of derivative instruments
Lesson 1: PutCall Parity
Due: January 23, 2017
Sufficient work must be shown to get credit for a correct answer. Partial credit may be given for
incorrect answers
ACTS 4308
FORMULA SUMMARY
Section 1: Calculus review and effective rates of interest and discount.
1. Some useful finite and infinite series:
(i) sum of the first n positive integers:
1 + 2 + + n =
n(n + 1)
2
(ii) finite geometric series:
1 rk+1
r rk+1
;
ACTS 6308
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 5
Section 9: Amortization of a loan.
Section 10: The sinking fund method of loan repayment.
Problem 1
Suppose that a $16,000 loan for a new car is to be repaid by level payments at the end of each
ACTS 6308
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 3
Section 5: Annuity valuation at any time point.
Section 6: Annuities with differing interest and payment period.
Problem 1
Frank makes deposits of 200 into an account at the beginning of each yea
ACTS 6308
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 2
Section 3. Force of interest, inflation.
Section 4. Annuityimmediate and annuitydue.
Problem 1
You are given that A(t) = Kt2 + Lt + M , for 0 t 2, and that A(0) = 105, A(1) = 114, and
A(2) = 12
ACTS 6308
Instructor: Yuly Koshevnik
SOLUTION TO HOMEWORK 1
Section 1. Calculus review and effective rates of interest and discount.
Section 2. Nominal rates of interest and discount.
Problem 1
On September 27, Eric deposits 100 into a savings account whi
ACTS 6308
Instructor: Yuly Koshevnik
HOMEWORK 4
Section 7: Annuities whose payments follow a geometric progression.
Section 8: Annuities whose payments follow an arithmetic progression.
Due: October 17, 2016
Sufficient work must be shown to get credit for
ACTS 6308
Instructor: Yuly Koshevnik
HOMEWORK 5
Section 9: Amortization of a loan.
Section 10: The sinking fund method of loan repayment.
Due: October 31, 2016
Sufficient work must be shown to get credit for a correct answer. Partial credit may be given f
ACTS 6308
Instructor: Yuly Koshevnik
HOMEWORK 7
Section 13: Measures of the rate of return on a fund.
Section 14: The term structure of interest rates, forward rates of interest and duration.
Due: December 5, 2016
Sufficient work must be shown to get cred