The absorbing stochastic matrix with states 0 , 5 , 1 , 2 , 3 and 4 .

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Answer 1

Question

Chapter 8.3, Problem 30E

(a)

To determine

The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

(b)

To determine

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

(c)

To determine

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

(d)

To determine

The particle begin at location 4 and find the expected number of times that it will be at location 0.

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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.)

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The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…

Answer 2

Question

Chapter 8.3, Problem 30E

(a)

To determine

The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

(b)

To determine

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

(c)

To determine

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

(d)

To determine

The particle begin at location 4 and find the expected number of times that it will be at location 0.

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Answer 3

Question

Chapter 8.3, Problem 30E

(a)

To determine

The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

(b)

To determine

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

(c)

To determine

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

(d)

To determine

The particle begin at location 4 and find the expected number of times that it will be at location 0.

Expert Solution & Answer

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Answer 4

Question

Chapter 8.3, Problem 30E

(a)

To determine

The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

(b)

To determine

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

(c)

To determine

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

(d)

To determine

The particle begin at location 4 and find the expected number of times that it will be at location 0.

Expert Solution & Answer

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Answer 5

Chapter 8.3, Problem 30E

(a)

To determine

The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

(b)

To determine

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

(c)

To determine

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

(d)

To determine

The particle begin at location 4 and find the expected number of times that it will be at location 0.

Answer 6

Chapter 8.3, Problem 30E

(a)

To determine

The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

Answer 7

Chapter 8.3, Problem 30E

(a)

To determine

The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

Answer 8

(b)

To determine

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

Answer 9

(b)

To determine

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

Answer 10

(c)

To determine

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

Answer 11

(c)

To determine

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

Answer 12

(d)

To determine

The particle begin at location 4 and find the expected number of times that it will be at location 0.

Answer 13

(d)

To determine

The particle begin at location 4 and find the expected number of times that it will be at location 0.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

The absorbing stochastic matrix with states 0 , 5 , 1 , 2 , 3 and 4 .

Solution Summary: The author explains how the absorbing stochastic matrix can be applied to a wide variety of fields such as statistical physics, finance, biology and psychology.

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The absorbing stochastic matrix with states 0,5,1,2,3 and 4.

To calculate: The stable matrix of the 051234051234[100.5000010000.50000.500000.500.500000.500.500000.50].

The probability that the particle would be begin at location 3 will eventually be absorbed at location 0.

The particle begin at location 4 and find the expected number of times that it will be at location 0.

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