Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Textbook Question
Chapter 2, Problem 2P
Repeat problem P2-I for the circuit shown in Fig. P22, which yields the
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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 2 Solutions
Introductory Mathematics for Engineering Applications
Ch. 2 - An analysis of a circuit shown in Fig. P2.1 yields...Ch. 2 - Repeat problem P2-I for the circuit shown in Fig....Ch. 2 - Repeat problem P2-I for the circuit shown in Fig....Ch. 2 - The current flowing through the inductor shown in...Ch. 2 - The voltage across the capacitor shown in Fig....Ch. 2 - In the purely resistive circuit shown in Fig....Ch. 2 - Repeat problem P2-6 if R=1600 and R2=R1+500.Ch. 2 - The energy dissipated by a resistor shown in...Ch. 2 - The equivalent capacitance C of two capacitors...Ch. 2 - Repeat problem P2-9 if C=75F and C2=C1+200F
Ch. 2 - The equivalent capacitance C of three capacitors...Ch. 2 - The equivalent inductance L of three inductors...Ch. 2 - Repeat problem R2-12 if L=150 mH and L1=L2+400 mH.Ch. 2 - The equivalent inductance L of three inductors...Ch. 2 - A model rocket is launched in the vertical plane...Ch. 2 - The ball shown in Fig. P2.16 is dropped from a...Ch. 2 - At time t=0, a hail is thrown vertically from the...Ch. 2 - To springs connected in series shown in Fig. P2.18...Ch. 2 - The equivalent stiffness of a series-parallel...Ch. 2 - An assembly of three springs connected in series...Ch. 2 - Consider a capacitor C and an inductor L connected...Ch. 2 - Assume that the total reactance in problem P2-21...Ch. 2 - If L=0.5 H. C=0.005 F, and the total reactance in...Ch. 2 - When converting resistances connected in a ∆...Ch. 2 - When converting resistances connected in a...Ch. 2 - When converting resistances connected in a ∆...Ch. 2 - When converting resistances connected in a...Ch. 2 - The characteristic equation of a series RLC...Ch. 2 - The characteristic equation of a parallel RLC...Ch. 2 - The characteristic equation of a mass, spring, and...Ch. 2 - The perimeter of an rectangle shown in Fig. P2.31...Ch. 2 - A diver jumps off a diving board 2.0 m above the...Ch. 2 - A level pipeline is required to pass through a...Ch. 2 - A research group is using a drop test to measure...Ch. 2 - The modulus of elasticity (E ) is a measure of a...Ch. 2 - Consider the following reaction having an...Ch. 2 - Consider the following reaction having an...Ch. 2 - An engineering co-op wants to hire an asphalt...Ch. 2 - Repeat problem P2-38 if the total area of the new...Ch. 2 - A city wants to hire a contractor to build a...
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