MATH 150 Exam Two Prof. Jambois
November 16, 2015
The exam has two parts. The first part consists of four multiple choice
questions. The second part consists of three non-multiple choice questions.
On the second part you must show all your work to receive
1 2 3 4 5 6 T
MATH 150
Exam Three with solutions
December 14, 2015
The exam consists of two parts. The first part is multiple choice. Circle the
correct answer. The second part is not multiple choice and you must show all
your work to receive full credit.
VIII. Rules for arithmetic for the rational numbers
Axioms for +
1. For any two numbers a,b there is a number a+b, their sum
2. (a+b)+c=a+(b+c)
3. There is a number called zero, written 0, which for any number is such that
a+0=a
4. For each number a there
Syllabus M1311 3 Credits Code 13319 Section TR11
Schedule TTH 11:00-12:15PM 1127 N
Text: Mathematical Ideas, Miller, Heeren, Hornsby, ISBN 13: 978-0-321-97707-6
Course Curriculum
Chapter
2. The Basic Concepts of Set
Theory
3. Introduction to Logic
1. T
patel (rpp467) Quest #7 Statics (part1/3) ha (51122013)
This print-out should have 13 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001 (part 1 of 2) 10.0 points
Consider an extended object (
castillo (ajc2686) Assignment 1 luecke (55035)
This print-out should have 20 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
10.0 points
which after expansion and simplication can
be rewrit
suddhi (ns8453) HW11 gilbert (55015)
This print-out should have 13 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
10.0 points
1
is the volume of the solid below the graph of
f having the r
1.
Evaluate the limit of
1 sec2 x
as x approaches 0.
Cosx 1
In Sin
tan
In Sin
lim
x 0 In tan
lim
x 0 In
Ans: -2
Solution:
In Sin
x 0 In tan
In Sin
lim
x 0 In tan
1 sec 2 x 2sec x sec x tan x
cos x 1
sin x
lim
2sec2 x tan x
sin x
2sin x
cos x cos2 xSinx
2
fu (ktf326) HW01 - Sect. 4.4 chavez-dominguez (55280)
This print-out should have 8 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
lim
x0
limit =
002
ln(6)
.
4
10.0 points
Determine if
6sin
Chapter 9
Numerical Methods for Option Pricing
Equation (8.26) provides a way to evaluate option prices. For some simple options,
such as the European call and put options, one can integrate (8.26) directly and obtain
a closed-form solution as in (8.18) o
Chapter 8
Black-Scholes Equations
1
The Black-Scholes Model
Up to now, we only consider hedgings that are done upfront. For example, if we write
a naked call (see Example 5.2), we are exposed to unlimited risk if the stock price rises
steeply. We can hedg
Chapter 10
Extensions of Black-Scholes Model
We have completed the Black-Scholes analysis of vanilla European call and put options in Chapter 8. Although the formulas presented are useful, there are many more
complicated situations in which the formulas a
Chapter 6
Geometric Brownian Motions
1
Normal Distributions
We begin by recalling the normal distribution briey. Let Z be a random variable
distributed as standard normal, i.e., Z N (0, 1). The probability density function of
Z is given by
2
1
(1)
pZ (z)
Chapter 7
Its Lemma
o
1
Its Lemma
o
Its lemma is the most important result (and tool) in doing stochastic analysis.
o
Roughly speaking, it relates the small change in a function of a random variable to
the small change in the random variable itself. In th
Chapter 5
Trading Strategies
1
Strategies Involving A Single Option and A Stock
One of the attractions of options is that they can be used to create a very wide range
of payo patterns. In the following we rst turn to several examples which involve a
singl
Chapter 1
Introduction
1
Acknowledgments
The rst seven chapters of this lecture notes were originally prepared by Prof. Xun Li of
the National University of Singapore (currently at Hong Kong Polytechnic University)
for the course Financial Mathematics I.
Chapter 2
Options
1
European Call Options
To consolidate our concept on European call options, let us consider how one can calculate the price of an option under very simple assumptions. Recall that the terminal
payo of a call option is c(T ) = max(S(T )
Chapter 4
Put-Call Parity
1
Bull and Bear
Financial analysts use words such as bull and bear to describe the trend in stock
markets. Generally speaking, a bull market is characterized by rising prices. Indeed,
an investor is sometimes called a bull when h
Chapter 3
Interest Rates and Forward
1
Interests and Present Values
When we put money in a bank, we earn interest. There are several types of interest.
First of all, there is the simple interest. Simple interest is when the interest you receive
is based o
Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam
Spring 2014
Instructions. You are allowed to use a two-sided 8.5 11 set of notes. You must show
all your work and cross out any work you do not want graded. Except on Problem 1, make
sure y
Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam Solutions
Spring 2011
1. (a) False; the two things have nothing to do with each other. The time series cfw_Xt
dened by Xt = N (t, 1) is Gaussian (since each random variable is normal), but
Brooklyn College
Department of Mathematics
Midterm Exam - Partial Solutions
Math 4506
Spring 2014
1. T, T, T, T, T, T, F, F, F
2. The easiest way to solve this problem is to note that Yt is in fact the AR(1) process
1
Yt = Yt1 + Zt
4
in its causal form.
(
Math 4506
Spring 2014
Homework 1 Solutions
Note: In some cases where the solution is straightforward, I may just write what the main idea
is to solve the problem. If you wish to know more, come and see me so we can talk about it.
1. This is nothing more t
Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam
Spring 2013
Instructions. You are allowed to use one 2-sided 8.5 11 sheet of notes, a calculator,
and a pen or pencil, but nothing else. In particular, if at any point of the exam you use
a
Math 4506
Spring 2014
Homework 2 Solutions
1. Textbook Problem 2.7: Since cfw_Yt is stationary, E[Yt ] = Y for all t and cfw_Yt has an autocovariance function Y . Therefore,
(a)
E[Wt ] = E[Yt Yt1 ] = E[Yt ] E[Yt1 ] = Y Y = 0.
Cov(Wt , Wt+h ) =
=
=
=
(1)
Math 4506
Spring 2014
Homework 3 Solutions
1. (a) The ACF of an MA(1) process has a non-zero value only at lags 1, 0, and 1. Problem
4.3 from the textbook (which you didnt do, so I didnt expect you to mention this)
shows that |(1)| 1 .
2
(b) The ACF of an
Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam
Spring 2011
Instructions. You are allowed to use a one-sided 8.5 11 set of notes. You must show
all your work and cross out any work you do not want graded. Except on Problems 1 and
2, make