Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Chapter 6.1, Problem 5E
In Problems
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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…
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.
Chapter 6 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - Prob. 7ECh. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...
Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - Using the Wronskian in Problems 15-18, verify that...Ch. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - Let L[y]:=y+y+xy, y1(x):=sinx, and y2(x):=x....Ch. 6.1 - Let L[y]:=yxy+4y3xy", y1(x)=cos2x, and y2(x):=1/3....Ch. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - Prob. 2ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - In Problems 15-18, find a general solution to the...Ch. 6.2 - Prob. 16ECh. 6.2 - In Problems 15 18, find a general solution to the...Ch. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - In Problems 1921, solve the given initial value...Ch. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - In Problems 22 and 23, find a general solution for...Ch. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Find a general solution to y3yy=0 by using Newtons...Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Higher-Order Cauchy-Euler Equations. A...Ch. 6.2 - Prob. 32ECh. 6.2 - On a smooth horizontal surface, a mass of m1 kg is...Ch. 6.2 - Suppose the two springs in the coupled mass-spring...Ch. 6.2 - Vibrating Beam. In studying the transverse...Ch. 6.3 - In Problems 1-4, use the method of undetermined...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - In Problems 31-33, solve the given initial value...Ch. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Use the annihilator method to show that if f(x) in...Ch. 6.3 - Prob. 37ECh. 6.3 - In Problems 38 and 39, use the elimination method...Ch. 6.3 - Prob. 39ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 2ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Given that {x,x1,x4} is a fundamental solution set...Ch. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.RP - Determine the intervals for which Theorem 1 on...Ch. 6.RP - Determine whether the given functions are linearly...Ch. 6.RP - Show that the set of functions...Ch. 6.RP - Find a general solution for the given differential...Ch. 6.RP - Find a general solution for the homogeneous linear...Ch. 6.RP - Prob. 6RPCh. 6.RP - Prob. 7RPCh. 6.RP - Use the annihilator method to determine the form...Ch. 6.RP - Find a general solution to the Cauchy-Euler...Ch. 6.RP - Find a general solution to the given Cauchy-Euler...
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