Mathematical Applications for the Management, Life, and Social Sciences
11th Edition
ISBN: 9781305108042
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Chapter 12.1, Problem 3E
To determine
To calculate: The function
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This problem is based on the fundamental option pricing formula for the continuous-time
model developed in class, namely the value at time 0 of an option with maturity T and
payoff F is given by:
We consider the two options below:
Fo=
-rT
= e
Eq[F].
1
A. An option with which you must buy a share of stock at expiration T = 1 for strike
price K = So.
B. An option with which you must buy a share of stock at expiration T = 1 for strike
price K given by
T
K =
T
St dt.
(Note that both options can have negative payoffs.) We use the continuous-time Black-
Scholes model to price these options. Assume that the interest rate on the money market
is r.
(a) Using the fundamental option pricing formula, find the price of option A. (Hint:
use the martingale properties developed in the lectures for the stock price process
in order to calculate the expectations.)
(b) Using the fundamental option pricing formula, find the price of option B.
(c) Assuming the interest rate is very small (r ~0), use Taylor…
Question 1. Prove that the function f(x) = 2; f: (2,3] → R, is not uniformly
continuous on (2,3].
Calculus III
May I please have the example, definition semicolons, and all blanks completed and solved?
Thank you so much,
Chapter 12 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 12.1 - 1. True or false:
(a)
(b)
Ch. 12.1 - Prob. 2CPCh. 12.1 - 1. If what is
Ch. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...
Ch. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 28ECh. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - Prob. 31ECh. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - Prob. 38ECh. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - 43. Revenue If the marginal revenue (in dollars...Ch. 12.1 - Prob. 44ECh. 12.1 - 45. Stimulus-response Suppose that when a sense...Ch. 12.1 - Prob. 46ECh. 12.1 - 47. Pollution A factory is damping pollutants into...Ch. 12.1 - 48. Population growth The rate of growth of the...Ch. 12.1 - 49. Average cost The DeWitt Company has found that...Ch. 12.1 - 50. Oil leakage An oil tanker hits a reef and...Ch. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - 54. Severe weather ice makers Hail is produced in...Ch. 12.1 - 55. U.S. population With U.S. Census Bureau data...Ch. 12.1 - 56. Consumer prices The consumer price index (CPI)...Ch. 12.2 - 1. Which of the following can be evaluated with...Ch. 12.2 - Prob. 2CPCh. 12.2 - 3. True or false: Constants can be factored...Ch. 12.2 - Prob. 4CPCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - In each of Problems 5 and 6, one of parts (a) and...Ch. 12.2 - In each of Problems 5 and 6, one of parts (a) and...Ch. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 18ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - 47. Revenue Suppose that the marginal revenue for...Ch. 12.2 - Prob. 46ECh. 12.2 - 49. Physical productivity The total physical...Ch. 12.2 - 50. Production The rate of production of a new...Ch. 12.2 - 51. Data entry speed The rate of change in data...Ch. 12.2 - Prob. 50ECh. 12.2 - 53. Film attendance An excellent film with a very...Ch. 12.2 - 54. Product quality and advertising An inferior...Ch. 12.2 - 55. Demographics Because of job outsourcing, a...Ch. 12.2 - 56. Franchise growth A new fast-food firm predicts...Ch. 12.3 - 1. True or false:
(a) (b)
(c) (d)
Ch. 12.3 - Prob. 2CPCh. 12.3 - Prob. 3CPCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Evaluate the integrals in Problems 1-32.
3.
Ch. 12.3 - Prob. 4ECh. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
9.
Ch. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Evaluate the integrals in Problems 1-32.
21.
Ch. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Evaluate the integrals in Problems 1-32.
29.
Ch. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - In Problems 37-40, a family of functions is given...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - 43. Revenue Suppose that the marginal revenue from...Ch. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - 46. Radioactive decay Radioactive substances decay...Ch. 12.3 - 47. Memorization The rate of vocabulary...Ch. 12.3 - Prob. 48ECh. 12.3 - 49. Compound interest If $P is invested for n...Ch. 12.3 - 50. Temperature changes When an object is moved...Ch. 12.3 - Prob. 56ECh. 12.4 - 1. True or false:
(a) If , then the constant of...Ch. 12.4 - Prob. 2CPCh. 12.4 - Prob. 3CPCh. 12.4 - Prob. 4CPCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - 14. Suppose that the marginal cost for a certain...Ch. 12.4 - 14. Suppose that the marginal cost for a certain...Ch. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Suppose that the marginal propensity to save is...Ch. 12.4 - Prob. 24ECh. 12.4 - Prob. 26ECh. 12.5 - Prob. 1CPCh. 12.5 - Prob. 2CPCh. 12.5 - Prob. 3CPCh. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - 41. Investing When the interest on an investment...Ch. 12.5 - Prob. 42ECh. 12.5 - 43. Bacterial growth Suppose that the growth of a...Ch. 12.5 - Prob. 44ECh. 12.5 - 46. Sales and pricing Suppose that a chain of auto...Ch. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - 48. Radioactive decay A certain radioactive...Ch. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - 51. Drug in an organ Suppose that a liquid carries...Ch. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Evaluate the integrals in Problems 1-26.
26. (a) ...Ch. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - 37. Oxygen levels in water The rate of change of...Ch. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Prob. 40RECh. 12 - 41. Cost The marginal cost for a product is
...Ch. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - 47. Fossil dating Radioactive beryllium is...Ch. 12 - Prob. 48RECh. 12 - Prob. 49RECh. 12 - Prob. 1TCh. 12 - Evaluate the integrals in Problems 1-11.
Ch. 12 - Prob. 3TCh. 12 - Prob. 4TCh. 12 - Prob. 5TCh. 12 - Prob. 6TCh. 12 - Prob. 7TCh. 12 - Prob. 8TCh. 12 - Prob. 9TCh. 12 - Prob. 10TCh. 12 - Prob. 11TCh. 12 - Prob. 12TCh. 12 - Prob. 13TCh. 12 - Prob. 14TCh. 12 - Prob. 15TCh. 12 - Prob. 16TCh. 12 - Prob. 17TCh. 12 - Prob. 18TCh. 12 - Prob. 19TCh. 12 - Suppose the marginal propensity to save is given...Ch. 12 - Prob. 21TCh. 12 - Prob. 22T
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