Nature of Mathematics
13th Edition
ISBN: 9781285697734
Author: karl J. smith
Publisher: Cengage Learning US
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Chapter 17.4, Problem 1PS
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To explain:
The Alabama paradox.
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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 17 Solutions
Nature of Mathematics
Ch. 17.1 - Prob. 1PSCh. 17.1 - Prob. 2PSCh. 17.1 - Prob. 3PSCh. 17.1 - Prob. 4PSCh. 17.1 - Prob. 5PSCh. 17.1 - Prob. 6PSCh. 17.1 - Prob. 7PSCh. 17.1 - Prob. 8PSCh. 17.1 - Prob. 9PSCh. 17.1 - Prob. 10PS
Ch. 17.1 - Prob. 11PSCh. 17.1 - Prob. 12PSCh. 17.1 - Prob. 13PSCh. 17.1 - Prob. 14PSCh. 17.1 - In voting among three candidates, the outcomes are...Ch. 17.1 - Prob. 16PSCh. 17.1 - Prob. 17PSCh. 17.1 - Prob. 18PSCh. 17.1 - Prob. 19PSCh. 17.1 - In voting among four candidates, the outcomes are...Ch. 17.1 - Prob. 21PSCh. 17.1 - In voting among four candidates, the outcomes are...Ch. 17.1 - In voting among four candidates, the outcomes are...Ch. 17.1 - Prob. 24PSCh. 17.1 - a.How many different ways can a voter rank 3...Ch. 17.1 - Prob. 26PSCh. 17.1 - How many different ways can a voter rank n...Ch. 17.1 - Prob. 28PSCh. 17.1 - Prob. 29PSCh. 17.1 - Prob. 30PSCh. 17.1 - In voting method among three candidates, the...Ch. 17.1 - Prob. 32PSCh. 17.1 - Prob. 33PSCh. 17.1 - Prob. 34PSCh. 17.1 - Twelve board members are voting on after-meeting...Ch. 17.1 - Prob. 36PSCh. 17.1 - Prob. 37PSCh. 17.1 - Prob. 38PSCh. 17.1 - Prob. 39PSCh. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Prob. 44PSCh. 17.1 - Prob. 45PSCh. 17.1 - Prob. 46PSCh. 17.1 - Seventeen people serve on a board and are...Ch. 17.1 - Seventeen people serve on a board and are...Ch. 17.1 - Prob. 49PSCh. 17.1 - Prob. 50PSCh. 17.1 - Prob. 51PSCh. 17.1 - Prob. 52PSCh. 17.1 - Prob. 53PSCh. 17.1 - Suppose your college transcripts show the...Ch. 17.1 - Prob. 55PSCh. 17.1 - Prob. 56PSCh. 17.1 - Prob. 57PSCh. 17.1 - Prob. 58PSCh. 17.1 - Prob. 59PSCh. 17.1 - Prob. 60PSCh. 17.2 - Prob. 1PSCh. 17.2 - Prob. 2PSCh. 17.2 - Prob. 3PSCh. 17.2 - Prob. 4PSCh. 17.2 - Prob. 5PSCh. 17.2 - Prob. 6PSCh. 17.2 - Prob. 7PSCh. 17.2 - Prob. 8PSCh. 17.2 - Prob. 9PSCh. 17.2 - Prob. 10PSCh. 17.2 - Prob. 11PSCh. 17.2 - Prob. 12PSCh. 17.2 - An election with three candidates has the...Ch. 17.2 - Prob. 14PSCh. 17.2 - Consider the following voting situation:...Ch. 17.2 - Consider the following voting situation:...Ch. 17.2 - Prob. 17PSCh. 17.2 - The philosophy department is selecting a...Ch. 17.2 - The Adobe School District is hiring a vice...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - Prob. 22PSCh. 17.2 - Prob. 23PSCh. 17.2 - Prob. 24PSCh. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - Prob. 29PSCh. 17.2 - A focus group of 33 people for ABCTV were asked to...Ch. 17.2 - Prob. 31PSCh. 17.2 - Prob. 32PSCh. 17.2 - Prob. 33PSCh. 17.2 - Prob. 34PSCh. 17.2 - Prob. 35PSCh. 17.2 - Prob. 36PSCh. 17.2 - Prob. 37PSCh. 17.2 - Prob. 38PSCh. 17.2 - HISTORICAL QUEST In 1993 the 101st International...Ch. 17.2 - The U.S. president is elected with a vote of the...Ch. 17.2 - HISTORICAL QUEST Article 7 of the French...Ch. 17.2 - A group of fun-loving people have decided to play...Ch. 17.2 - A group of fun-loving people have decided to play...Ch. 17.2 - Prob. 44PSCh. 17.2 - Prob. 45PSCh. 17.2 - The fraternity is electing a national president,...Ch. 17.2 - The fraternity is electing a national president,...Ch. 17.2 - The fraternity is electing a national president,...Ch. 17.2 - Prob. 49PSCh. 17.2 - Consider an election with three candidates with...Ch. 17.2 - Consider an election with four candidates with the...Ch. 17.2 - Prob. 52PSCh. 17.2 - Consider an election with four candidates with the...Ch. 17.2 - Prob. 54PSCh. 17.2 - Consider an election with three candidates with...Ch. 17.2 - Prob. 56PSCh. 17.2 - Prob. 57PSCh. 17.2 - Prob. 58PSCh. 17.2 - Prob. 59PSCh. 17.2 - The Game of WIN Construct a set of nonstandard...Ch. 17.3 - Prob. 1PSCh. 17.3 - Prob. 2PSCh. 17.3 - Prob. 3PSCh. 17.3 - IN YOUR OWN WORDS What is the quota rule? Does...Ch. 17.3 - Prob. 5PSCh. 17.3 - Prob. 6PSCh. 17.3 - Prob. 7PSCh. 17.3 - Prob. 8PSCh. 17.3 - Prob. 9PSCh. 17.3 - Prob. 10PSCh. 17.3 - Modified quotas are given in Problems 714. Round...Ch. 17.3 - Prob. 12PSCh. 17.3 - Prob. 13PSCh. 17.3 - Prob. 14PSCh. 17.3 - Find the standard divisor to two decimal places...Ch. 17.3 - Prob. 16PSCh. 17.3 - Prob. 17PSCh. 17.3 - Prob. 18PSCh. 17.3 - Prob. 19PSCh. 17.3 - Prob. 20PSCh. 17.3 - Prob. 21PSCh. 17.3 - Prob. 22PSCh. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - Consider the populations given in Problems 2932....Ch. 17.3 - Consider the populations given in Problems 2932....Ch. 17.3 - Consider the populations given in Problems 29-32....Ch. 17.3 - Consider the populations given in Problems 29-32....Ch. 17.3 - Consider the populations given in Problems 33-36....Ch. 17.3 - Consider the populations given in Problem. a.Find...Ch. 17.3 - Prob. 35PSCh. 17.3 - Prob. 36PSCh. 17.3 - Prob. 37PSCh. 17.3 - Prob. 38PSCh. 17.3 - Prob. 39PSCh. 17.3 - Prob. 40PSCh. 17.3 - Consider the following apportionment problem for...Ch. 17.3 - Prob. 42PSCh. 17.3 - Prob. 43PSCh. 17.3 - Consider the following apportionment problem for...Ch. 17.3 - Prob. 45PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Prob. 47PSCh. 17.3 - Prob. 48PSCh. 17.3 - Prob. 49PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Prob. 54PSCh. 17.3 - Prob. 55PSCh. 17.3 - Prob. 56PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Prob. 58PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.4 - Prob. 1PSCh. 17.4 - Prob. 2PSCh. 17.4 - Prob. 3PSCh. 17.4 - Prob. 4PSCh. 17.4 - Prob. 5PSCh. 17.4 - Prob. 6PSCh. 17.4 - Prob. 7PSCh. 17.4 - Prob. 8PSCh. 17.4 - Prob. 9PSCh. 17.4 - Prob. 10PSCh. 17.4 - Prob. 11PSCh. 17.4 - Prob. 12PSCh. 17.4 - Prob. 13PSCh. 17.4 - Prob. 14PSCh. 17.4 - Prob. 15PSCh. 17.4 - Prob. 16PSCh. 17.4 - Prob. 17PSCh. 17.4 - Prob. 18PSCh. 17.4 - Prob. 19PSCh. 17.4 - Prob. 20PSCh. 17.4 - Prob. 21PSCh. 17.4 - Prob. 22PSCh. 17.4 - Prob. 23PSCh. 17.4 - Prob. 24PSCh. 17.4 - Prob. 25PSCh. 17.4 - In Problems 2326, apportion the indicated number...Ch. 17.4 - Prob. 27PSCh. 17.4 - Prob. 28PSCh. 17.4 - Prob. 29PSCh. 17.4 - Prob. 30PSCh. 17.4 - Prob. 31PSCh. 17.4 - Prob. 32PSCh. 17.4 - Prob. 33PSCh. 17.4 - Prob. 34PSCh. 17.4 - Prob. 35PSCh. 17.4 - Prob. 36PSCh. 17.4 - Prob. 37PSCh. 17.4 - Prob. 38PSCh. 17.4 - Prob. 39PSCh. 17.4 - Prob. 40PSCh. 17.4 - Prob. 41PSCh. 17.4 - Prob. 42PSCh. 17.4 - Prob. 43PSCh. 17.4 - Prob. 44PSCh. 17.4 - Prob. 45PSCh. 17.4 - Prob. 46PSCh. 17.4 - Prob. 47PSCh. 17.4 - Prob. 48PSCh. 17.4 - Prob. 49PSCh. 17.4 - Prob. 50PSCh. 17.4 - Prob. 51PSCh. 17.4 - Prob. 52PSCh. 17.4 - Prob. 53PSCh. 17.4 - In problems 54-56, suppose the annual salaries of...Ch. 17.4 - In problems 54-56, suppose the annual salaries of...Ch. 17.4 - Prob. 56PSCh. 17.4 - Prob. 57PSCh. 17.4 - An elderly rancher died and left her estate to her...Ch. 17.4 - Prob. 59PSCh. 17.4 - Prob. 60PSCh. 17.CR - Prob. 1CRCh. 17.CR - Prob. 2CRCh. 17.CR - Prob. 3CRCh. 17.CR - Prob. 4CRCh. 17.CR - Prob. 5CRCh. 17.CR - Prob. 6CRCh. 17.CR - Prob. 7CRCh. 17.CR - Prob. 8CRCh. 17.CR - Prob. 9CRCh. 17.CR - Prob. 10CRCh. 17.CR - Prob. 11CRCh. 17.CR - Prob. 12CRCh. 17.CR - Chemistry is taught at five high schools in the...Ch. 17.CR - Prob. 14CRCh. 17.CR - Prob. 15CRCh. 17.CR - Prob. 16CRCh. 17.CR - Prob. 17CRCh. 17.CR - Prob. 18CRCh. 17.CR - Prob. 19CRCh. 17.CR - Prob. 20CR
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- Please 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_forward5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward
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