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Washington - AMATH - 541
1.11. FORWARD CONTRACTSReading: Luenberger Chapter 10Prerequisite: Interest rates. Read (review)Luenberger Chapter 4.9/29/111.1 Forward Contracts A Forward Contract is an agreement between two partiesto buy/sell an asset at an agreed upon price at
Washington - AMATH - 541
2. FUTURES AND HEDGINGReadingLuenberger, Chapter 10.1 - 10.4, 10.6, 10.7, 10.9,10.10NOTE: Standard reference for future reading: Hull,J. C. (2011), Options, Futures and Other Derivatives,8th edition, Pearson/Prentice Hall.9/28/20112.12.22.0 Reca
Washington - AMATH - 541
3.13. Optimal Hedge RatiosUsing Hull (2011) notation rather than Luenberger (1998)SFSFchange in spot price over life of hedgechange in futures price over life of hedgestandard deviation of Sstandard deviation of Fcorrelation between S and FHed
Washington - AMATH - 541
4. Op&ons Reading: Chapter 12, Chapter 11 of Luenberger 14.1 Options types A call is an option to buy A put is an option to sell A European option can be exercised onlyat the end of its life An American option can be exercised atany tim
Washington - AMATH - 541
6. PORTFOLIO THEORYReading: Luenberger Chapter 6 Consider a portfolio of n assets (e.g. stocks). Aportfolio is constructed by weighting asset i by weightwi .Stock picking is accomplished by increasing theweight of the stock that you like, and setting
Washington - AMATH - 541
7. Capital Asset Pricing MODELReading: Luenberger Chapter 710/19/20111Sharpe (1964), Lintner (1965)Nobel Prize: Sharpe (1990) Based on Mean Variance Portfolio Optimization Rules for how to invest (normative economics) Main Result Under Equilibrium
Washington - AMATH - 541
8. CAPM and Factor ModelsReading: Luenberger Chapter 8We will first do single factor model and then do multifactor model.Single-factor model also illustrates how we can obtainthe beta estimates for use in CAPM.A criticism of CAPM is that there is onl
Washington - AMATH - 541
9. UTILITY FUNCTIONSReading: Luenberger, Chapter 9(Many of the slides in this lecture are modificationsfrom last years course by Professor Martin)10/29/1119.1 EXPECTED UTILITY FRAMEWORKWOWU(w)E[U(W)]Initial Wealth (fixed)End of Period Wealth (
Washington - AMATH - 541
5. Binomial Tree ModelReading: Chapter 12, Chapter 11 ofLuenberger15.1 A Toy Model That Could Later Be MadeVery Realistic Suppose a stock is currently at price S. In a later time t, it could move up and down,but only to one of the two known states
Washington - AMATH - 541
Derivation of Ordinary Linear SquareEstimatorsA factor model for y i ( the subscript could denote time;then it is a time series) :y i = + xi + ix i are the regressors (factors),and and are the regression coefficients that need to be estimated. are
Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
90Chapter 5Banach SpacesMany linear equations may be formulated in terms of a suitable linear operatoracting on a Banach space. In this chapter, we study Banach spaces and linear operators acting on Banach spaces in greater detail. We give the denitio
Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
Chapter 8Bounded Linear Operators on a HilbertSpaceIn this chapter we describe some important classes of bounded linear operators onHilbert spaces, including projections, unitary operators, and self-adjoint operators.We also prove the Riesz represent
Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
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Washington - AMATH - 567
Errata Applied Analysis (Corrected in online les but not in Second Printing) p. 115: Replace statement of Theorem 5.53 with: A consistent approximation scheme is convergent if and only if it is stable. p.115: Replace last paragraph (Conversely.) of the pr
Washington - AMATH - 567
Indexbackwards heat equation, 164Baker-Campbell-Hausdor formula, 123ballclosed, 14open, 14unit, 4Banach algebra, 39Banach space, 8, 91of linear operators, 110Banach-Alaoglu theorem, 120, 208Banach-Steinhaus theorem, 204base of open sets, 84ba
Washington - AMATH - 567
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Washington - AMATH - 581
AMATH 581 Autumn Quarter 2011Homework 1: Quantum Harmonic OscillatorDUE: Friday, October 14, 2011 (actually at 3am on 10/15)The probability density evolution in a one-dimensional harmonic trapping potential is governed by the partialdierential equatio
Washington - AMATH - 581
AMATH 581 Autumn Quarter 2011Homework 2: Quantum Harmonic OscillatorDUE: Friday, October 21, 2011 (actually at 3am on 10/22)Continuing on the idea of the harmonic oscillator of Homework 1:(b) Calculate the rst ve normalized eigenfunctions (n ) and eig
Washington - AMATH - 581
AMATH 581 Autumn Quarter 2011Homework 3: Vorticity-Streamfunction EquationsDUE: Friday, November 4, 2011 (actually at 3am on 11/5)The time evolution of the vorticity (x, y, t) and streamfunction (x, y, t) are given by the governing equations:t + [, ]
Washington - AMATH - 581
AMATH 581 Autumn Quarter 2011Homework 4: Vorticity-Streamfunction EquationsDUE: Friday, November 11, 2011 (actually 3 a.m. on 11/12)The time evolution of the vorticity (x, y, t) and streamfunction (x, y, t) are given by the governing equations:t + [,
Washington - AMATH - 581
AMATH 581 Autumn Quarter 2011Homework 5: Reaction-Diusion SystemsDUE: Tuesday, November 22, 2011 (actually Wednesday, 11/23 at 3 a.m.)Consider the reaction-diusion systemUt = (A)U (A)V + D12UVt = (A)U + (A)V + D2where A2 = U 2 + V 2 and22V22
Washington - AMATH - 581
AMATH 581 Autumn Quarter 2011Homework 6: Bose-Einstein Condensation in 3DDUE: Wednesday, December 7, 2011 (actually Thursday, 12/8 at 3 a.m.)Consider the Gross-Pitaevskii system (nonlinear Schrodinger with potential) modeling a condensedstate of matte
Washington - AMATH - 581
AMATH 581Practice 1: Autumn 2011DUE: midnight, Thursday 10/6I Consider the functionf (x) = x sin(3x) exp(x)and solve for the x-value near x 0.5 that satises f (x) = 0. In the rst part, usethe Newton-Raphson method with the initial guess x(1) = 1.6 t
Washington - AMATH - 582
AMATH 582Computation Methods forData AnalysisJ. Nathan KutzMarch 14, 2010AbstractThis course is a survey of computational methods used for extractingmeaningful results out of experimental or computational data. The central focus is on using a combi
Washington - AMATH - 582
AMATH 582 Winter Quarter 2012Homework 1: An ultrasound problemDUE: Friday, Jan. 20, 2012You dog uy swallowed a marble. The vet suspects that it has now worked its way into the intestines. Usingultrasound, data is obtained concerning the spatial variat
Washington - AMATH - 582
AMATH 582 Winter Quarter 2012Homework 2: Gbor transformsaDUE: Friday, Feb. 3, 2012Part IIn this homework, you will analyze a portion of Handels Messiah with time-frequency analysis.To get started, you can use the following commands (note that Handel
Washington - AMATH - 582
AMATH 582 Winter Quarter 2012Homework 3: Saving Derek ZoolanderDUE: Wednesday, Feb. 15, 2012GQ is doing a feature article on VH1s 3-time male model of the year Derek Zoolander. Much to everybeautiful persons dismay, the ridiculously good looking photo
Washington - AMATH - 582
AMATH 582 Winter Quarter 2012Homework 4: PCADUE: Wednesday, Feb. 22, 2012On the webpage are movie les created from three dierent cameras (videos are from 2011). The experimentsare an attempt to illustrate various aspects of the PCA and its practical u
Washington - AMATH - 582
AMATH 582 Winter Quarter 2012Homework 5: Music Genre IdenticationDUE: Friday, Mar. 9, 2012Music genres are instantly recognizable to us, wether it be jazz, classical, blues, rap, rock, etc.One can always ask how the brain classies such information and
Washington - AMATH - 500F
Boundary Value '1!Problems ofibMathematical PhysicsdiDownloaded on 24 May 2011 to 173.250.143.104. Redistribution subject to SIAM license or copyright; see http:/www.siam.org/journals/ojsa.phpSIAM's Classics in Applied Mathematics series consists of b
Washington - AMATH - 500F
Boundary Value C"i!Problems ofb Mathematical PhysicsDownloaded on 24 May 2011 to 173.250.143.104. Redistribution subject to SIAM license or copyright; see http:/www.siam.org/journals/ojsa.phpSIAM's Classics in Applied Mathematics series consists of bo
Washington - FIN - 350
FV = PV ( 1 + r )PV =CFrEAC = a = enPV =11 n (1+ r ) NPV11n r r ( 1+ r ) ED+ dD+ED+EE[ Ri ] = rf + i ( E[ Rm ] rf )2 =FVn( 1+ r )PV =n FV ln PV n= ln ( 1 + r ) 1 FV n r = 1 PV CF1rNPV = CF0 +PV =CF1( 1 + r1 )E
Washington - FIN - 350
FV = PV ( 1 + r )nPV =PV =CF 11 r ( 1+ r ) n PV =CF1rPV =NPV = CF0 +( 1 + r1 )1 + effective rate = ( 1 + r )nCF =CF1rgCF1( 1+ r )+PV11n r r ( 1+ r ) 1 + Real =CF2( 1 + r2 )2 FV ln PV n= ln(1 + r ) 1n FV 1r= PV FV
University of Toronto - ECO - 365
ECO365Topic 5National Income AccountsandBalance of PaymentsOverview Our goal is to study how a shock in one country affectseconomic activity in other countries. But in order to do that, we should be able to develop a measure of economic activity
University of Toronto - ECO - 365
ECO365Topic 6Output and Exchange Rate in theShort RunOverview Until now, our study of exchange rates has been largelydisconnected from the rest of the economy. In particular, we took the economys level of output asgiven. In this chapter, we shall
University of Toronto - ECO - 364
The nal impact of integration on rm prots depends on two forces:1. A negative competition effect: Integration leads to an immediate increase in thetotal number of rms in the market, which has a negative effect on prots.2. A positive market size effect
University of Toronto - ECO - 364
ECO 364 - Topic 6Trade PolicyKunal DasguptaDasgupta (UofT)Trade Policy1 / 43Road map1Motivation2Taris and quotas under perfect competition3Taris and quotas under imperfect competition4Export subsidy5World Trade Organization (WTO)Dasgupta
University of Toronto - ECO - 364
Taris and quotas under perfect competitionOptimal TariA large country can gain by imposing a tari. But what level of tarimaximizes this gain? The optimal tari.Starting from free trade, a small tari initially increases welfarebecausethe height and th
University of Toronto - ECON - 365
ECO365Topic 7The Choice of Exchange Rate Regime and The EuroOverview1. 2. 3.The Case of Britain and its peg The determinants of an exchange rate regime The theory of optimum currency areas4. The conditions for joining Eurozone 5.Assessing the Euro
Kaplan University - ENGLISH - CS 113
My Ideal JobWhat would my Ideal job be, well lets see I have always wanted to be a coach of some sortwhether I am coaching football, basketball, or baseball etc. No matter what that particular sportis I want to coach it. The reason behind this is becau
Truman State - CHEM - 1411
General Chemistry 1(Chem -1411)Chem 14111Significant figure(a) 24.61178round off : 24.612 g(b) 1259.89218(c) 41.0947Chem 1411round off : 1260 g/Lround off : 41.1 mLSignificant FigureFinal answer: 427 mi/hChem 1411Unit FactorChem 1411Chemi
Phoenix - HUM/111 - 111
HUM 111 assignmentThis is a hard choice to make because at the same time while we are drilling we are getting oilthat is needed for other purposes but I do agree that we need to go green no matter what Ibelieve we need to look at both sides of the situ
Phoenix - HUM/111 - 111
HUM 111 DQ 3In the last few years, the use of blogs, wikis, and other types of sharing websitessuch asYouTube, Facebook, MySpace, and Twitterhave become increasingly popular as a means ofexpressing oneself and spreading news, opinions, or ideas. What k
Phoenix - HUM/111 - 111
HUM 111 DQ 4Define throbbing from Ch. 3 of The Art of Thinking. What strategies you can use to preventyourself from the practice of throbbing?Throbbing is when people think the opinion that pleases them and then believe it.The strategies that one can
Clark State Community College - ACCT - 241
Question 11 out of 1 pointsWhich of thefollowing may causemanagement tointentionallyunderstate profits?AnswerSelectedAnswer:All of theabove.Question 21 out of 1 pointsWhich of thefollowing is true.AnswerSelected Answer:Question 31 out o
Clark State Community College - ACCT - 241
Question 11 out of 1 pointsWhich of thefollowing is not doneduring the clientselection andretention phase ofplanning?AnswerSelected Answer:Question 21 out of 1 pointsWhich of thefollowing is notincluded in theengagement letter?AnswerSelec
Clark State Community College - ACCT - 241
Question 11 out of 1 pointsAn entity's internalcontrol consists ofthe policies andproceduresestablished to providereasonable assurancethat specific entityobjectives will beachieved. Only someof these objectives,policies, andprocedures arerel
Clark State Community College - ACCT - 241
Question 11 out of 1 pointsThe cash account isinvolved in whichcycle?AnswerSelectedAnswer:All of theabove.Question 21 out of 1 pointsWhich of thefollowing is anappropriate auditprogram step for thereview of canceledchecks for authorizeds
Clark State Community College - ACCT - 241
Question 11 out of 1 pointsTo be recognized,revenues must beAnswerSelectedAnswer:All the above.Question 21 out of 1 pointsRecording a salewhile keeping thegoods in your ownwarehouse is called:AnswerSelectedAnswer:Bill and hold.Question 3
Clark State Community College - ACCT - 241
Question 11 out of 1 pointsA "voucher" is aAnswerSelectedAnswer:None of theabove.Question 21 out of 1 pointsA "blind purchaseorder" is aAnswerSelected Answer:Question 31 out of 1 pointsWhich of thefollowing accounts isnot included in the