Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 1.3, Problem 1E
To determine
Whether the statement
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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 1 Solutions
Discrete Mathematics
Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...
Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - A small purse manufacturer has a single machine...Ch. 1.1 - What is the answer to the previous problem if the...Ch. 1.1 - A survey is to be made of grocery shoppers in Los...Ch. 1.2 - In Exercises 1–16, calculate the number...Ch. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - In Exercises 1–16, calculate the number...Ch. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - A baseball manager has decided who his 9 starting...Ch. 1.2 - A president, vice president, and treasurer are to...Ch. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Different prizes for first place, second place,...Ch. 1.2 - Prob. 23ECh. 1.2 - A farmer with 7 cows likes to milk them in a...Ch. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - A dinner special for 4 diners at a Chinese...Ch. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Show that if 0 ≤ 2r ≤ n, then .
Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Suppose that the rating/kilogram ratio is computed...Ch. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - How many subsets does {Dopey, Happy, …, Doc}...Ch. 1.3 - How many subsets does {Chico, Harpo, Groucho,...Ch. 1.3 - Prob. 24ECh. 1.3 - Suppose m and n are positive integers with m < n....Ch. 1.3 - Prob. 26ECh. 1.3 - A draw poker player may discard some of his 5...Ch. 1.3 - Suppose that in the previous problem no more than...Ch. 1.3 - How long would it take a computer that can check...Ch. 1.3 - Find a subset of the 12 experiments with a total...Ch. 1.4 - In Exercises 1–6, tell whether the given...Ch. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - In Exercises 1–6, tell whether the given...Ch. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - Prob. 13ECh. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - In Exercises 15–18, make a table listing the...Ch. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - In Exercises 19–22, illustrate as in Example 1.5...Ch. 1.4 - In Exercises 19–22, illustrate as in Example 1.5...Ch. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - In Exercises 23–26, estimate how long a computer...Ch. 1.4 - In Exercises 27–30, tell how many elementary...Ch. 1.4 - In Exercises 27–30, tell how many elementary...Ch. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1 - Prob. 1SECh. 1 - Prob. 2SECh. 1 - Prob. 3SECh. 1 - Prob. 4SECh. 1 - Prob. 5SECh. 1 - Prob. 6SECh. 1 - Prob. 7SECh. 1 - Prob. 8SECh. 1 - Prob. 9SECh. 1 - Prob. 10SECh. 1 - Prob. 11SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 13SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 15SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 17SECh. 1 - In Cincinnati, chili consists of spaghetti topped...Ch. 1 - Five students decide to send a delegation to a...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20-23, tell whether each expression...Ch. 1 - Let P(x) = 3x3+4x−5. Compute the various values S...Ch. 1 - Repeat the previous problem, using Horner's...Ch. 1 - Let S = {1, 2, 3, 4}. Find the ordered sequence of...Ch. 1 - Illustrate the use of the bubble sort algorithm to...Ch. 1 - How long would it take a computer to do 25!...Ch. 1 - Apply the following algorithm to n = 18.
What is...Ch. 1 - Prob. 30SECh. 1 - Prob. 1CPCh. 1 - Prob. 2CPCh. 1 - Prob. 3CPCh. 1 - Prob. 4CPCh. 1 - Prob. 5CPCh. 1 - Prob. 6CPCh. 1 - Prob. 9CPCh. 1 - Prob. 10CP
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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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