EP CALCULUS FOR BUSINESS..-MYLAB ACCESS
14th Edition
ISBN: 9780135961438
Author: Barnett
Publisher: PEARSON CO
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Chapter 10.3, Problem 26E
To determine
To find: The Taylor series at 0 for
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4. Assume that a risk-free money market account is added to the market described in Q3.
The continuously compounded rate of return on the money market account is log (1.1).
(i) For each given μ, use Lagrange multipliers to determine the proportions (as a
function of μ) of wealth invested in the three assets available for the minimum
variance portfolio with expected return μ.
(ii) Determine the market portfolio in this market and calculate its Sharp ratio.
3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free
asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05,
Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75.
(i) Given that an investor is targeting a total expected return of μ = 0.2. What
portfolio weights should they choose to meet this goal with minimum portfolio
variance? Correct all your calculations up to 4 decimal points.
(ii) Determine the global minimum-variance portfolio and the expected return and
variance of return of this portfolio (4 d.p.).
(iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient
frontier.
(iv) Without further calculation, explain how the minimum variance of the investor's
portfolio return will change if the two risky assets were independent.
2. A landlord is about to write a rental contract for a tenant which lasts T months. The
landlord first decides the length T > 0 (need not be an integer) of the contract, the
tenant then signs it and pays an initial handling fee of £100 before moving in. The
landlord collects the total amount of rent erT at the end of the contract at a continuously
compounded rate r> 0, but the contract stipulates that the tenant may leave before T,
in which case the landlord only collects the total rent up until the tenant's departure
time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r.
(i) Calculate the expected total payment EW the landlord will receive in terms of T.
(ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides
that the rental rate r should depend on the contract length T by
r(T)
=
λ
√T
1
For each given λ, what T (as a function of X) should the landlord choose so as to
maximise their expected utility? Justify your answer.
Hint. It might be…
Chapter 10 Solutions
EP CALCULUS FOR BUSINESS..-MYLAB ACCESS
Ch. 10.1 - Find the nth derivative of f(x)=lnx.Ch. 10.1 - Prob. 2MPCh. 10.1 - Prob. 3MPCh. 10.1 - Find the second-degree Taylor polynomial at a = 8...Ch. 10.1 - Prob. 5MPCh. 10.1 - Prob. 1EDCh. 10.1 - (A)Let p(x) be a polynomial of degree n 1....Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3E
Ch. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - In Problems 1316, find f(3)(x). 15.f(x)=exCh. 10.1 - In Problems 1316, find f(3)(x). 16.f(x)=xCh. 10.1 - Prob. 17ECh. 10.1 - In Problems 1720, find f4(x). 18.f(x)=e5xCh. 10.1 - Prob. 19ECh. 10.1 - In Problems 1720, find f4(x). 20.f(x)=12+xCh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - In Problems 2128, find the indicated Taylor...Ch. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Use the third-degree Taylor polynomial at 0 for...Ch. 10.1 - Prob. 41ECh. 10.1 - Use the third-degree Taylor polynomial at 4 for...Ch. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - Prob. 55ECh. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Prob. 59ECh. 10.1 - Prob. 60ECh. 10.1 - Prob. 61ECh. 10.1 - Prob. 62ECh. 10.1 - Prob. 63ECh. 10.1 - Prob. 64ECh. 10.1 - Prob. 65ECh. 10.1 - Prob. 66ECh. 10.1 - Prob. 67ECh. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.1 - Prob. 71ECh. 10.1 - Consider f(x) = ln (1 + x) and its third-degree...Ch. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - Prob. 76ECh. 10.1 - Prob. 77ECh. 10.1 - Prob. 78ECh. 10.1 - Prob. 79ECh. 10.1 - Prob. 80ECh. 10.1 - Prob. 81ECh. 10.1 - Average price. Given the demand equation...Ch. 10.1 - Prob. 83ECh. 10.1 - Prob. 84ECh. 10.1 - Prob. 85ECh. 10.1 - Prob. 86ECh. 10.1 - Prob. 87ECh. 10.1 - Prob. 88ECh. 10.1 - Prob. 89ECh. 10.1 - Prob. 90ECh. 10.1 - Prob. 91ECh. 10.1 - Prob. 92ECh. 10.1 - Prob. 93ECh. 10.1 - Prob. 94ECh. 10.1 - Prob. 95ECh. 10.1 - Prob. 96ECh. 10.1 - Prob. 97ECh. 10.1 - Prob. 98ECh. 10.2 - Prob. 1MPCh. 10.2 - Prob. 2MPCh. 10.2 - Prob. 3MPCh. 10.2 - Prob. 1EDCh. 10.2 - (A)The six functions pn(x)=1+x++xn, n = 1, 2, , 6,...Ch. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - (A) Graph the nth-degree Taylor polynomials at 0...Ch. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - In Problems 3338, find the nth-degree Taylor...Ch. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - Prob. 42ECh. 10.2 - (A) Find the interval of convergence of the Taylor...Ch. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - Problems 4750 require a basic knowledge of the...Ch. 10.3 - Prob. 1MPCh. 10.3 - Find the Taylor series at 0 for f(x) = 3x3 ln(1 ...Ch. 10.3 - Prob. 3MPCh. 10.3 - Prob. 4MPCh. 10.3 - Prob. 5MPCh. 10.3 - Prob. 6MPCh. 10.3 - Prob. 7MPCh. 10.3 - Prob. 8MPCh. 10.3 - Prob. 1EDCh. 10.3 - Prob. 2EDCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Solve the problems by performing operations on the...Ch. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Find the Taylor series at 0 for (A) f(x)=x1x2 (B)...Ch. 10.3 - Prob. 35ECh. 10.3 - If f(x) satisfies f(x) = ln (1 + x2) and f(0) = 1,...Ch. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Prob. 60ECh. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.4 - Prob. 1MPCh. 10.4 - Prob. 2MPCh. 10.4 - Prob. 3MPCh. 10.4 - Prob. 4MPCh. 10.4 - Prob. 1EDCh. 10.4 - Suppose you wish to use a Taylor series for...Ch. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - In Problems 938, use Theorem 1 to perform the...Ch. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - In Problems 4548, use the second-degree Taylor...Ch. 10.4 - Prob. 46ECh. 10.4 - In Problems 4548, use the second-degree Taylor...Ch. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - To estimate 01.511+x2dx a student takes the first...Ch. 10.4 - There are different ways to approximate a function...Ch. 10.4 - There are different ways to approximate a function...Ch. 10.4 - In Problems 5566, use Theorem 1 to perform the...Ch. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Useful life. A computer store rents time on...Ch. 10.4 - Average price. Given the demand equation...Ch. 10.4 - Temperature. The temperature (in degrees Celsius)...Ch. 10.4 - Temperature. Repeat Problem 61 for...Ch. 10.4 - Prob. 63ECh. 10.4 - Prob. 64ECh. 10.4 - Prob. 65ECh. 10.4 - Prob. 66ECh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Use Theorem 1 of Section 10.2 to find the interval...Ch. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - In Problems 10 and 11, use the formula an =...Ch. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - In Problems 25 and 26, use the second-degree...Ch. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - In Problems 27 and 28, use a Taylor polynomial at...Ch. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Medicine. The rate of healing for a skin wound (in...Ch. 10 - Prob. 42RECh. 10 - Prob. 43RE
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- Please solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward
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