IEOR 4701
Assignment 4
2014 Fall
Due on next Wednesday, Oct. 22 in class
1. Let cfw_X(t) : t 0be a continuous time Markov chain with the following transition rate matrix
0
0
A=
1
2
3
4
2
1
1
2
3
1
2
1
Assignment 3
IEOR 4701 - Stochastic Models for Financial Engineering
Due October 1st, in class
1. Gamblers ruin problem.
We have two gamblers, A and B. We toss a coin: if it comes up H, then B pays 1
IEOR 4701 Lecture Notes - Lecture 26
Applications to the Optional Sampling Theorem
Optional sampling theorem (O.S.T.) states that, with regularity conditions, the
expectation of a martingale at a stop
IEOR 4701 Lecture Notes - Lecture 24
Further Topics in Martingale
The theory of martingale came into being with the aim of providing insight into the
apparent impossibility of making money by placing
IEOR 4701 Lecture Notes - Lecture 22
Itos Lemma and applications
Itos Lemma is the key result in stochastic calculus. In this lecture we state and give an
outline proof of a general form of the result
IEOR 4701 Lecture Notes - Lecture 18
We rst show that Brownian motion is a Markov process. To see this is true, suppose cfw_X(t)
is a BM (, ). It is easy to see
Pcfw_X(t + s) [y, y + dy]|X(s) = x
=Pcf
IEOR 4701 Lecture Notes - Lecture 15
Recall in the last lecture we construct a sequence of binomial processes W (t) that converge to a geometric Brownian motion as 0. We start by introducing
1
1
w.p.
IEOR 4701 Lecture Notes - Lecture 13
Recap - Continuous Time Markov Chain
1. We have constructed a Continuous Time Markov Chain using transition rate matrix
A.
2. Consider a call option with a payo fu
Assignment 7
IEOR 4701 - Stochastic Models for Financial Engineering
Due date: Monday, Dec. 8th 2014. (Question 6 is extra-credit. All questions are
equally weighted.)
Exercise 1: Consider a model of
Assignment 5
IEOR 4701 - Stochastic Models for Financial Engineering
Due November 5, in class
1. Recall that if X Gamma(, ) for , > 0, then
fX (x) =
ex x1
I(x > 0).
()
(a) Verify that if < , then
(
E