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21-270
Introduction to Mathematical Finance
D. Handron
Exam #1 Review
The exam will be closed book and notes; only the following calculators will be permitted:
TI-30X IIS, TI-30X IIB, TI-30Xa.
1. (25
Recitation 21
21-127 Concepts of Math
11.08.2011
Lecture material Divisibility, factorization, and modular arithmetic:
Throughout these denitions and theorems, assume all variables are integers, unles
21270 Introduction to Mathematical Finance D. Handron
Exam #3 A
April 18, 2014 Name: 3447»;
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Closed book and notes; only the following calculators will be permitted: TI30X IIS,
TI30XS MultiVieW, TI-3
21-270 Introduction to Mathematical Finance D. Handron
Exam #2 , \
March 19, 2014 - Name: Sahib ans.
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Closed book and notes; only the following calculators will be permitted: TI30X IIS,
TI-SOXS
63
Part II Solutions
SOLUTIONS FOR PART II
5. COMBINATORIAL REASONING
5.1. When rolling n dice, the probability is 1/2 that the sum of the numbers
obtained is even. There are 6n equally likely outcome
1
Part I Solutions
SOLUTIONS FOR PART I
1. NUMBERS, SETS, AND FUNCTIONS
1.1. We have at least four times as many chairs as tables. The number of
chairs (c) is at least () four times the number of tabl
Recitation 21
21-127 Concepts of Math
11.08.2011
Problems and (some) solutions
Congruence sense: Let x, y, a, b Z and n N. Assume x y mod n. Prove that ax + b ay + b
mod n.
Solution: We can use the d
183
Chapter 13: The Real Numbers
SOLUTIONS FOR PART IV
13. THE REAL NUMBERS
13.1. Sequences.
a) x dened by x n = n is monotone but not bounded. Each succeeding
term is larger than the previous term, s
to the average of the spot rates R*(1) and R* (2), which were computed
in part Therefore, we assume
RR (1.5) = 12*(1) 312,42)
= 4.56%.
Under this assumption about R*(1.5), determine the price Z at t =
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Chapter 2
Fixed-Income Securities and
Interest Rates
We now begin a systematic study of xed-income securities and interest rates. By a
xed-income security we mean a nancial instrument that promises xe
Course Notes for Introduction to Mathematical
Finance (21-270)
William J. Hrusa & Dmitry Kramkov
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
January 10, 2011
2
183
Chapter 13: The Real Numbers
SOLUTIONS FOR PART IV
13. THE REAL NUMBERS
13.1. Sequences.
a) x dened by x n = n is monotone but not bounded. Each succeeding
term is larger than the previous term, s
70-100 Global Business
Homework 1: Fall 2017
Due Wednesday, September 27, 2017
9. The market in which the currency of one country is exchanged for the currency of another 3pts.
a. Foreign currency
b.
Recitation 21
21-127 Concepts of Math
11.08.2011
Problems and (some) solutions
Congruence sense: Let x, y, a, b Z and n N. Assume x y mod n. Prove that ax + b ay + b
mod n.
Solution: We can use the d
125
Chapter 9: Probability
SOLUTIONS FOR PART III
9. PROBABILITY
9.1. If A B , then P ( A) P ( B )TRUE. P ( B ) is the sum of the probabilities assigned to points in A plus the sum of the proabilities