S17 Stochastic Methods in Finance: Homework 4
Due Wednesday April 5
1. Let B and W be independent Brownian motions. Consider stochastic processes X, Y with the following
dynamics
dXt = dt + dBt
dYt =
G6501-001, Fall 2015: Homework set 2
Due Monday October 12
1. Page 119, Exercise 3.7.
2. Assume that X is a random variable on (, F, P). Let Q P be another probability measure on (, F)
with Radon-Niko
G6501 Stochastic Processes: Lecture 1
Yuchong Zhang
Wednesday September 9, 2015
Acknowledgement: I would like to thank Mattias Jonsson, Sergey Nadtochiy, Philip
Protter and Hongzhong Zhang for sharing
Chapter 9
It Calculus
o
c
2015 Lars Tyge Nielsen All Rights Reserved Do not post or circulate
This chapter denes It processes and integration with respect to It proo
o
cesses, explains Its lemma, and
Chapter 8
Stochastic Integrals
c
2015 Lars Tyge Nielsen All Rights Reserved Do not post or circulate
8.1
Stochastic Integrals Preliminaries
In this section, we dene and study the stochastic integral
3
i
\Mbgtw/Le'ifwmw : &</\A>of Maw {34 meg-milkij MMTVMJM LJ
A : g» 0, x6 d Ex/Ll Tawim r Wed/$9
J40 moat Jim at amJ-e enigma); XI: cm Nm,3jr4c%
ABM; WC? O/mok TA:M£§1~>O/XE¢A}
"LA (MA XI}? OVUZ M
/& X Lcjcu>a
X>tL) « 1 .4 "'1
~ «1 Lafa, z .4 h "M _ A»: M
g E; _ i7 Sc (9. .7; 010C : fajita
m r reigl A
:1 an) é 2. C "a; ma.
aura}?
éf Ls} Kw ,-7>(W MA Mgi)
M ' " m
/g :3 X: X NJNM)
M T) ,
v,» W§
FINAL EXAM
STOCHASTIC PROCESSES AND APPLICATIONS
Unless otherwise stated B = (Bt , Ft )t0 is one-dimensional standard
Brownian motion starting at zero
3
1. Prove that Yt = Bt 3tBt is a martingale
2. U
STOCHASTIC PROCESSES
(1) A certain town never has two sunny days in a row. Each day is classied
as being either sunny, cloudy (but dry), or rainy. If it is sunny one day,
then it is equally likely to
S17 Stochastic Methods in Finance: Homework 2
Due Wednesday February 15
1. The price S per share of Fish stock is modeled using a two-period binomial model. We have S0 = 48,
S1 (H) = 54, S1 (T ) = 45,
S17 Stochastic Methods in Finance: Homework 3
Due Wednesday March 1
Submit your solution as a hardcopy but the spreadsheet must be submitted on Canvas
1. For this problem you need to find a source for
S17 Stochastic Methods in Finance: Homework 1
Due Wednesday February 1
1. Consider a European derivative security with the following payo structure V = V (S) as a function of
the underlying asset S:
8