Math 3589
Introduction to Financial Mathematics
Homework Assignment #1 Due September 6
1. Suppose S0 = 4, S1 (H) = 8, S1 (T ) = 2 and the risk-free interest rate
is r = 0. Someone is willing to buy or
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #2 Due Tuesday January 26
1. A stock currently costs $4 per share. In each time period, the value of the
stock will eith
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #2 Solutions
1. A stock currently costs $4 per share. In each time period, the value of the
stock will either increase o
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #1 Due January 19 Solutions
1. Suppose S0 = 4, S1 (H) = 8, S1 (T ) = 2 and r = 0. The price of a European
Call option wi
Name:
MATH 3589 INTRODUCTION TO FINANCIAL MATHEMATICS
SPRING 2016 MIDTERM 1
No books, notes or electronic devices.
Show your work and explain your answers.
1. (20 points)
(a) Dene a convex function (d
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #3 February 2 Solutions
1. Let (, P) be a finite probability space. Recall that if A is an event,
then the probability o
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #4 Solutions
1. Consider the N-period binomial model. Let 0 , 1 , . . . , N 1 be any adapted
portfolio process. In other
Math 3589
Introduction to Financial Mathematics
Homework Assignment #4 Solutions
1. Consider the Binomial Asset pricing model as in Chapter 1, except that, after each movement in the stock price, a di
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #3 Due Tuesday, February 2
1. Let (, P) be a nite probability space. Recall that if A is an event,
then the probability
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #1 Due January 19
1. Suppose S0 = 4, S1 (H) = 8, S1 (T ) = 2 and r = 0. The price of a European
Call option with strike
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #6 Due Tuesday, March 1
1. Under the conditions of Theorem 3.1.1, show the following analogues of
properties (1)(3):
1
Math 3589
Fall 2017
Introduction to Financial Mathematics
Homework Assignment #8
Due Tuesday, October 31
1. Let Z0 , Z1 , . . . ZN be the Radon-Nikod
ym derivative process on the coin flip
space
= cf
Math 3589
Introduction to Financial Mathematics
Homework Assignment #6 Solutions
1. Under the conditions of Theorem 3.1.1, show the following analogues of
properties (1)(3):
1 > 0) = 1
(1) P(
Z
1] =
Math 3589
Introduction to Financial Mathematics
Homework Assignment #3 Due Tuesday, September 20
1. Consider the N-period binomial model. Let 0 , 1 , . . . , N 1 be any adapted
portfolio process. In o
Math 3589
Introduction to Financial Mathematics
Homework Assignment #11
1. Prove that a symmetric random walk is a martingale.
2. Prove that a symmetric random walk is a Markov process.
2
3. Prove tha
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #8 Solutions
Exercise 16. Consider the two period binomial model, with the stock price
at time t = 0, S0 = 4, the up fac
Math 3589
Introduction to Financial Mathematics
Homework Assignment #9 Due November 8
1. Prove the Optimal Sampling theorem, Part I: A martingale stopped at
a stopping time is a martingale. A supermar
Math 3589
Introduction to Financial Mathematics
Homework Assignment #2 Due Tuesday September 13
1. (Put-call parity) A stock currently costs S0 per share. In each time period,
the value of the stock w
Math 3589
Fall 2017
Introduction to Financial Mathematics
Solutions Homework Assignment #4 Due Tuesday, September 19
1. Text, Exercise 2.3.
Solution.
We assume M0 , M1 , . . . , MN is a martingale, so
Name:
MATH 3589
MIDTERM 1
INTRODUCTION TO FINANCIAL MATHEMATICS
FALL 2017
SEPTEMBER 14, 2017 2:20 - 3:40 PM JENNINGS 60
SOLUTIONS
No books, notes or electronic devices.
Show your work and explain your
Math 3589 Fall 2017 Introduction to
Financial Mathematics
Solutions Homework Assignment #3 Due Tuesday, September 12
1. Text, Exercise 2.1.
Solution.
This exercise asks you to compute some elementary
MATH 3589
INTRODUCTION TO FINANCIAL MATHEMATICS
FALL 2017
MIDTERM 2
OCTOBER 17, 2017 2:20 - 3:40 PM JENNINGS 60
SOLUTIONS
No books, notes or electronic devices.
Show your work and explain your answers
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #11 Solutions
1. Consider the three period (N = 3) binomial model with S0 = 4, the up
factor u = 2, the down factor d =
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #4 Due Tuesday, February 16
1. Consider the N-period binomial model. Let 0 , 1 , . . . , N 1 be any adapted
portfolio pr
Math 3589
Spring 2016
Introduction to Financial Mathematics
Homework Assignment #5 Due Tuesday, February 22
1. Consider the Binomial Asset pricing model as in Chapter 1, except that, after each moveme
Name:
MATH 3589
HOMEWORK
MIDTERM 2
No books, notes or electronic devices.
Show your work and explain your answers.
1. (20 points)
e are two positive probability measures on a finite sample space , def
Math 3589
Introduction to Financial Mathematics
Homework Assignment #6 Due Tuesday, October 17
1. Under the conditions of Theorem 3.1.1 (Properties of the RN Derivative),
show the following analogues
Math 3589
Introduction to Financial Mathematics
Homework Assignment #4 Due Tuesday, September 27
1. Consider the Binomial Asset pricing model as in Chapter 1, except that, after each movement in the s