MATH IN OUR WORLD (LOOSELEAF)-W/ACCESS
3rd Edition
ISBN: 9781259969690
Author: sobecki
Publisher: MCG
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Textbook Question
Chapter 13.3, Problem 33E
For Exercises 31–34, use the nearest neighbor method to approximate the optimal solution. Start at vertex A in each case.
31. 
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Students have asked these similar questions
Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro-
priate for pricing options in practice. Give one reason that would substantiate this claim?
Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager
asks you to pick only one of them to invest in based on the model provided. Which one do you
choose and why ?
Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price
at time t of a European put with maturity T and strike price K. Then, the discounted option
price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.)
Question 4. You are considering pricing an American put option using a Black-Scholes model
for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no
more than 2 sentences), explain how you would proceed to price it.
Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the
interest rate…
In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i,
and i.
(a) Verify the relations between this roots and the coefficients of the polynomial.
(b) Find the annulus region in which the roots lie.
Chapter 13 Solutions
MATH IN OUR WORLD (LOOSELEAF)-W/ACCESS
Ch. 13.1 - Prob. 1TTOCh. 13.1 - The floor plan shown in Figure 14-7 is for a...Ch. 13.1 - Prob. 3TTOCh. 13.1 - Draw a graph for my neighborhood, shown in Figure...Ch. 13.1 - Prob. 5TTOCh. 13.1 - Prob. 6TTOCh. 13.1 - Prob. 7TTOCh. 13.1 - Prob. 8TTOCh. 13.1 - Prob. 1ECh. 13.1 - What is the difference between a loop and a...
Ch. 13.1 - What is the difference between a circuit and a...Ch. 13.1 - Draw two graphs that look physically different but...Ch. 13.1 - Prob. 5ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - How does graph coloring apply to maps?Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 18ECh. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 20ECh. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 29ECh. 13.1 - Prob. 30ECh. 13.1 - For Exercises 3134, represent each figure using a...Ch. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - For Exercises 3538, draw a graph to represent each...Ch. 13.1 - Prob. 38ECh. 13.1 - Prob. 39ECh. 13.1 - For Exercises 3942, draw a graph that represents...Ch. 13.1 - Prob. 41ECh. 13.1 - Prob. 42ECh. 13.1 - In Exercises 4350, use graph coloring to find the...Ch. 13.1 - Prob. 44ECh. 13.1 - Prob. 45ECh. 13.1 - Prob. 46ECh. 13.1 - In Exercises 4350, use graph coloring to find the...Ch. 13.1 - Prob. 48ECh. 13.1 - Prob. 49ECh. 13.1 - Prob. 50ECh. 13.1 - Prob. 51ECh. 13.1 - Prob. 52ECh. 13.1 - Prob. 53ECh. 13.1 - Prob. 54ECh. 13.1 - Prob. 55ECh. 13.1 - Draw a graph that represents the street map in...Ch. 13.1 - Prob. 57ECh. 13.1 - Prob. 58ECh. 13.1 - Prob. 59ECh. 13.1 - Prob. 61ECh. 13.1 - Prob. 62ECh. 13.1 - Prob. 63ECh. 13.1 - (a)When a graph represents a map as in Exercise...Ch. 13.2 - Classify the paths shown in the graphs as Euler...Ch. 13.2 - Use Euler's theorem to determine if the graphs...Ch. 13.2 - Prob. 3TTOCh. 13.2 - Prob. 4TTOCh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - For Exercises 710, decide whether each connected...Ch. 13.2 - Prob. 10ECh. 13.2 - For Exercises 710, decide whether each connected...Ch. 13.2 - Prob. 12ECh. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 14ECh. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 16ECh. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 18ECh. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 20ECh. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Prob. 25ECh. 13.2 - Prob. 26ECh. 13.2 - Prob. 27ECh. 13.2 - For Exercises 2126, draw a graph for the figures...Ch. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - For Exercises 33 and 34, determine if an Euler...Ch. 13.2 - For Exercises 33 and 34, determine if an Euler...Ch. 13.2 - Prob. 37ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Draw some sample graphs and use them to discuss...Ch. 13.2 - Prob. 42ECh. 13.2 - Prob. 43ECh. 13.2 - Prob. 44ECh. 13.2 - Prob. 45ECh. 13.2 - Explain why the word connected is crucial...Ch. 13.2 - Prob. 47ECh. 13.2 - Prob. 48ECh. 13.3 - Prob. 1TTOCh. 13.3 - Prob. 2TTOCh. 13.3 - Prob. 3TTOCh. 13.3 - The driving times in minutes between four cities...Ch. 13.3 - Prob. 5TTOCh. 13.3 - Prob. 6TTOCh. 13.3 - Prob. 7TTOCh. 13.3 - What is the difference between a Hamilton path and...Ch. 13.3 - Prob. 2ECh. 13.3 - Give an example of a problem in our world that can...Ch. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Describe what a typical traveling salesperson...Ch. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - For Exercises 1118, find two different Hamilton...Ch. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - For Exercises 1118, find two different Hamilton...Ch. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - For Exercises 1118, find two different Hamilton...Ch. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Prob. 24ECh. 13.3 - For Exercises 1924, find two different Hamilton...Ch. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - For Exercises 2528, find the number of Hamilton...Ch. 13.3 - Prob. 30ECh. 13.3 - Prob. 31ECh. 13.3 - For Exercises 29 and 30, use the brute force...Ch. 13.3 - For Exercises 3134, use the nearest neighbor...Ch. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - Prob. 37ECh. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - Prob. 40ECh. 13.3 - Prob. 41ECh. 13.3 - For Exercises 3942, use the information in the...Ch. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - For Exercises 4346, use the information in the...Ch. 13.3 - For Exercises 4346, use the information in the...Ch. 13.3 - For Exercises 45–48, use the information in the...Ch. 13.3 - Prob. 49ECh. 13.3 - A pizza delivery person has five prearranged...Ch. 13.3 - Prob. 51ECh. 13.3 - Prob. 52ECh. 13.3 - Prob. 53ECh. 13.3 - Prob. 54ECh. 13.3 - When planning routes, distance isnt always the key...Ch. 13.3 - Prob. 56ECh. 13.3 - Repeat questions 51 through 54, choosing four...Ch. 13.3 - Prob. 58ECh. 13.3 - Prob. 59ECh. 13.3 - Prob. 60ECh. 13.3 - Find a road atlas that has a mileage chart. Pick...Ch. 13.3 - Prob. 62ECh. 13.3 - Prob. 63ECh. 13.3 - Prob. 64ECh. 13.3 - Prob. 65ECh. 13.3 - Prob. 66ECh. 13.3 - Prob. 67ECh. 13.3 - Prob. 68ECh. 13.3 - Prob. 69ECh. 13.3 - Prob. 70ECh. 13.3 - Prob. 71ECh. 13.3 - Prob. 72ECh. 13.3 - Prob. 73ECh. 13.3 - Prob. 74ECh. 13.4 - Prob. 1TTOCh. 13.4 - Prob. 2TTOCh. 13.4 - Prob. 3TTOCh. 13.4 - Prob. 4TTOCh. 13.4 - Prob. 5TTOCh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - For Exercise 716, decide whether or not each graph...Ch. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Prob. 11ECh. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Prob. 21ECh. 13.4 - Prob. 22ECh. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Prob. 31ECh. 13.4 - Prob. 32ECh. 13.4 - Prob. 33ECh. 13.4 - As a new suburban neighborhood is being built, the...Ch. 13.4 - Prob. 35ECh. 13.4 - Prob. 36ECh. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - Prob. 39ECh. 13.4 - In the last two sections, we used both Hamilton...Ch. 13.4 - Prob. 41ECh. 13.4 - Prob. 42ECh. 13.4 - Prob. 43ECh. 13.4 - Prob. 44ECh. 13 - Use the graph shown in Figure 14-62 for Exercise...Ch. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Use the graph shown in Figure 14-62 for Exercises...Ch. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Repeat Exercise 13 for the graphs from Exercises...Ch. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - For the following graph: (a)What is the degree of...Ch. 13 - Draw a graph with two bridges, and the...Ch. 13 - Prob. 3CTCh. 13 - Prob. 4CTCh. 13 - (a)For the graph shown in Figure 14-73, find an...Ch. 13 - Prob. 6CTCh. 13 - For the housing plan shown in Figure 14-75, draw a...Ch. 13 - Prob. 8CTCh. 13 - Use the brute force method to find the shortest...Ch. 13 - Use the nearest neighbor method and cheapest link...Ch. 13 - Prob. 11CTCh. 13 - Decide whether the problem can be solved using...
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