This website uses cookies to ensure you have the best experience. Learn more

Netscape Ipo Essay

1431 words - 6 pages

Advanced Financial Models
Example sheet 1 - Michaelmas 2010

Michael Tehranchi

Problem 1. In a one-period model, a num´raire asset is called risk-free if its time-1 price
is not random: if asset i is risk-free, then S1 = (1 + ri )S0 for a real constant ri > −1, called
the risk-free rate of return. Suppose that a market model has at least one risk-free asset.
Show that if there is no arbitrage, then the risk-free rate of return is unique, in the sense
that if both asset i and asset j are risk-free then ri = rj .
Problem 2. (Binomial model) Consider a market with two assets. Asset 0 is a risk-free
bond with
B0 = 1, and B1 = 1 + r
for some constant interest rate r > −1, ...view middle of the document...

Fix a
constant vector α ∈ Rd and define an equivalent measure Q on (Ω, F ) by the density
= eα·W −|α| /2 .
Prove that the random variable W = W − α has the Nd (0, I ) distribution under Q.
Problem 7. Consider a d + 1 asset model, where asset 0 is cash B0 = 1 = B1 while assets
1, . . . , d have time-1 prices S1 with the Nd (µ, V ) distribution, where µ ∈ Rd and V is a
positive semi-definite d × d matrix. Use the previous problem to show that there is no
arbitrage if V is non-singular. Show that there might be arbitrage (depending on the values
of µ and S0 ) if V is singular.
Problem 8. (Stiemke’s theorem) Let A be a m × n matrix. Prove that exactly one of the
following statements is true:
• There exists an x ∈ Rn with xi > 0 for all i = 1, . . . , n such that Ax = 0.
• There exists a y ∈ Rm with (AT y )i ≥ 0 for all i = 1, . . . , n such that AT y = 0.
What does this have to do with finance?
Problem 9. Let X1 , . . . , Xd be d random variables. We aim to show that if
a · X ≥ 0 a.s. for some a ∈ Rd ⇒ a · X = 0 a.s.
then there exists a random variable Z > 0 a.s. such that E(Z |Xi |) < ∞ and E(ZXi ) = 0 for
all i.
(1) Why does the above theorem imply the hard direction of the 1FTAP?
(2) Why is there no loss of generality in assuming that the random variables X1 , . . . , Xd
are linearly independent in the sense that if b · X = 0 a.s. then b = 0.
(3) Let F (a) = E(ea·X −|X | ). Show that F is finite-valued and smooth.
(4) We aim now to show that there exists a∗ ∈ Rd which minimizes F . Assuming this

for the moment, show that Z = ea ·X −|X | satisfies the conclusions of the statement.
(5) Now suppose for the sake of finding a contradiction that F does not achieve its
minimum. Let (an )n be such that F (an ) ↓ inf a F (a). Why can we assume that (an )n
is unbounded?
(6) Let an = an /|an |. Why does the sequence (ˆn ) have a convergent subsequence?
(7) Suppose |an | → ∞ and an → α. Show that P(α · X > 0) = 0.
(8) Use the hypothesis of the statement to show α · X = 0 a.s. Why is this our desired
Problem 10. Let X1 , . . . , Xd and Y random variables, and let
Z = {Z > 0 a.s. : E(Z |Xi |) < ∞ and E(ZXi ) = 0 for all i} = ∅.

We aim to show that if E(ZY ) = 0 for all Z ∈ Z such that E(Z |Y |) < ∞, then
Y = a · X a.s. for some a ∈ Rd .
(1) Why does this statement imply the hard direction of the characterization of attainable
(2) How can we modify the argument in the previous problem to find random variables
Zr ∈ Z of the form
Zr = ear ·X +rY −|X | −Y
for r ∈ {0, 1}.
(3) Show that Y = b · X + log(Z1 /Z0...

Other assignments on Netscape Ipo

Hospitals Paper

6014 words - 25 pages I hope to provide in this paper a comprehensive understanding for what the term “hospital” has become. Hospitals are an extremely complex system that man has created and shaped and reshaped throughout history. My goal in writing and researching this paper will be to provide those who read it a clear understanding on how the hospital system got to where it is today, and to shed some light on the many organizations that affiliate with and

Course Syllabus Essay

2610 words - 11 pages [pic] COURSE SYLLABUS Semester: Fall, Year: 2012  College Mission Statement Richard J. Daley College provides high-quality education which leads to academic success, career development, and personal enrichment that fulfill diverse community needs. Mathematics Department Mission Statement Our mission is to deliver excellent service and to provide learning opportunities by offering a wide range of mathematics courses, which will help our


1477 words - 6 pages Boeing Management Planning Heather Oetzel MGT 330 October 22, 2012 Joe Cheng Abstract Boeing is known as “the world’s leading aerospace company and the largest manufacturer of commercial jetliner and military aircraft combined ("The Boeing Company: About Us", 2012). Every company uses different types of management techniques including how the planning function of management is used. Planning allows organizations to develop how the

Assisted Suicide

1015 words - 5 pages Should physician-assisted suicide be legal? While I believe if one chooses to end his or own life through physician assistance for reasons that they chose, the choice should be up to the individual. Physician-assisted suicide should be at one's discretion. “Assisted Suicide, also called Voluntary Euthanasia, is currently a contentious issue in many countries. Because Euthanasia is legal in a few modern democracies: the Netherlands, Belgium

Tanglewood Case 1

797 words - 4 pages Tanglewood’s staffing strategy requires the organization to make key decisions about the acquisition, deployment, and retention of the organization’s workforce. In order to accomplish this, Tanglewood’s must make thirteen decisions regarding its staffing levels and its staffing quality. One of the first decisions that Tanglewood needs to choose is to acquire or develop talent. Tanglewood should try to develop their current talent because one


1391 words - 6 pages Есе по въпроса: Кои от всички „действащи” лица могат да се разглеждат като морално отговорни и в какво именно? по казуса Форд „Пинто” Корпоративните злодеяния са нанесли повече вреди на обществото от всички улични престъпления взети заедно. Според данни на ФБР сумата от уличните престъпления възлиза на $3.8 млрд. годишно, а загубите от корпоративните измами между $100 млрд. и $400 млрд. годишно

The Penis

1052 words - 5 pages The short story ”The Penis” is written by Hanif Kureishi. The short story is about a penis, which has been separated from its owner Doug, who we hear from later on. At first though we hear about a guy called Alfie who was “a cutter – a hairdresser – and had to get to work”. He is having breakfast with his wife, when she asks him what he did last night, and if he had a good time last night? Alfie can not remember what he did last night, he then

Managed Care Paper

543 words - 3 pages Managed Care and Case Management Care Marvin Lloyd BSHS/402-Case Management 27 August 2012 Virgil Miller Managed Care are techniques employed to help reduce the cost for providing health benefits and a system for improving organizations quality of care


439 words - 2 pages The life expectancy is lower; so people are not kept alive with drugs for decades in a virtual sleep state. There is less state education; so kids don't have it drilled into them that their only goal in life is to make money, at the cost of 'everything' else. The health care is less; so diseases, usually brought by Westerners, kill many more than they do in countries where drug companies can make a fortune from selling medicines that aren't

Chapter 6 International Business

7113 words - 29 pages CGGGG The Political Economy of International Trade Chapter Outline OPENING CASE: Why Are Global Food Prices Soaring? INTRODUCTION INSTRUMENTS OF TRADE POLICY Tariffs Subsides Country Focus: Subsidized Wheat Production in Japan Import Quotas and Voluntary Export Restraints Local Content Requirements Administrative Polices Antidumping Policies Management Focus: U.S. Magnesium

Scope And Goals

279 words - 2 pages Introduction: Kudler Fine Foods is a specialty food store based in San Diego, California with its three locations in La Jolla, Del Mar, and Encinitas. Kudler Fine food prides itself on offering fresh and organic products that are carefully selected from local farmers and around the world. The organization has recently taken the initiative to start a Frequent Shopper Program to market and increase sales. This program will offer the customers a

Similar Documents

Nasdaq Bubble Essay

846 words - 4 pages stock valuations really did take on tulip bulb characteristics. The foundation for the high-tech bubble was laid in late 1995, when Netscape went public, raising approximately $ 2 billion in its IPO and making Jim Clark the first internet billionaire. Not only was that figure dramatic, the offering broke new ground in the sense that Netscape had no earnings. In the past, P/E ratios for new companies may have been unrealistically high, but at

Mgt216 Essay

714 words - 3 pages The first ethical issue presented in the ethics game simulation was whether to warn consumers about the contaminated product and what information to provide consumers about the contaminant. The second ethical issue was whether to sell a product that does not meet U.S. safety requirements in a foreign market that has lower safety restrictions. G-BioSport was not required to meet prior approval from the Federal Drug Administration before they

Economy Effect Of Marijuana Essay

277 words - 2 pages Modern American History by Alan Renga 2nd Mid Term! You will be given 3 Short Essay questions and 20 Multiple Choice questions deriving from this list! 80 points total! The 1920s Warren Harding then Calvin Coolidge Tea Pot Dome 1st Red Scare Immigration Restriction, Sacco and Vanzetti Langston Hughes, Marcus Garvey, KKK Prosperity, advertising Prohibition, Al Capone Flappers, Clara Bow, Rudolph Valentino Babe Ruth, Jack Dempsey

The Vc Shakeout Essay

2033 words - 9 pages 10.4 US M&A VALUE EU M&A VALUE US IPO VALUE EU IPO VALUE 6.5 $54.1B AVERAGE IPO # OF YEARS 2.4 $858M $4B 1.8 2000 Q1 2010 SOURCE DOW JONES VENTURESOURCE 4,027 $19B $11.1B $8.8B Q1 2010 2000 6.4 AVERAGE M&A # OF YEARS 5.4 Q1 2010 SOURCE DOW JONES VENTURESOURCE SOURCE THOMSON REUTERS VCs are finding fewer promising start-ups: The total number and value of investments in 2009 (2,800 deals, $17 billion) reached their lowest point