Question: Suppose that X1,X2, . . . is a lognormal geometric random walk with parameters (, 2). More specifically, suppose that Xk = X0exp(r1 +

Suppose that X1,X2, . . . is a lognormal geometric random walk with parameters (μ, σ2). More specifically, suppose that Xk = X0exp(r1 + ∙ ∙ ∙ +rk), where X0 is a fixed constant and r1, r2, . . . are i.i.d. N(μ, σ2).
(a) Find P(X2 > 1.3X0).
(b) Use (A.4) to find the density of X1.
(c) Find a formula for the 0.9 quantile of Xk for all k.
(d) What is the expected value of X2k for any k? (Find a formula giving the expected value as a function of k.)
(e) Find the variance of Xk for any k.

Step by Step Solution

★★★★★

3.44 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Part a For this we have Pr 1 r 2 log13 1 Pr 1 r 2 log13 1 pnormlog13mean 2 sd 2 Part b F... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

957-M-S-L-R (8446).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Suppose that two observations X1 and X2 are drawn at random from a uniform distribution with the following p.d.f.: where the value of is unknown ( > 0). Determine the M.L.E. of for each of the...

Suppose that you are interested in estimating the ceteris paribus relationship between y and xi. For this purpose, you can collect data on two control variables, x2 and x3 (For concreteness, you...

Suppose that a point (X1, X2, X3) is chosen at random, that is, in accordance with the uniform p.d.f., from the following set S: S = {(x1, x2, x3): 0 xi 1 for i = 1, 2, 3}. Determine: a. Pr[X1 ...

8. Suppose that X1, X2,... is a lognormal geometric random walk with parameters (, 2). More specifically, suppose that Xk = X0 exp(r1 + + rk), where X0 is a fixed constant and r1, r2,... are i.i.d....

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Planning Demand and Supply in a Supply Chain Capacity Planning and Assignment 1 utdallas.edu/~metin Outline Capacity Planning Product-to-plant Assignment utdallas.edu/~metin 2 Deterministic Capacity...

1 . Is the production function f ( x 1 , x 2 ) = x 1 / 2 1 x 3 / 4 2 constant returns, increasing returns, or decreasing returns to scale? 2 . Suppose x 1 and x 2 are used in fixed proportions and f...

#1 STA355H1F due Wednesay, October 5, 2016 Problems to hand in: 1. Suppose that X1 , , Xn are independent Exponential random variables with density f (x; ) = exp(x) for x 0 where > 0 is an unknown...

Its macroeconomic questions could you help me solve it Question One The convolution formula is a useful trick when we are interested in the sum or average of independent random variables. In the last...

2 STAT 330: Mathematical Statistics Winter 2016 Assignment 2 Name: ID: Due on Feb 29th (Monday) 11:30am in drop boxes across the hall from MC 4065/4066. 1 1. [7 marks] Let f (x, y) = kxy 2 , if 0 x...

SKILLS O EMPLOYABILITY SKILLS Scenario: DG Ltd G Ltd manufactures gaming consoles for ado- years age. The management accountant, Mrs Ruva Tamic, is keen to keep a tight control over the costs as she...

Selection rules for spectral transitions of atoms where Russell-Saunders coupling is valid are (Bethe and Jackiw, Chapter 11) L = 0, ± 1; S = 0; J = 0, ± 1 (but J = 0 to J = 0 is...

Brand valuations are critical to CeOs, financial and marketing executives, security analysts, institutional investors, and others who depend on well-researched, reliable information needed for...

Business Ethics on a Global Scale. In the 1990s, Pfizer, Inc., developed a new antibiotic called Trovan (trovafloxacin mesylate). Tests showed that in animals Trovan had life-threatening side...

Consider the wire bond pull strength data in Exercise 12-8. (a) Test for significance of regression using a = 0.05. Find the P-value for this test. What conclusions can you draw? (b) Calculate the...

Data on National Hockey League team performance was presented in Exercise 12-11. (a) Test the model from this exercise for significance of regression using a = 0.05. What conclusions can you draw?...

An article entitled A Method for Improving the Accuracy of Polynomial Regression Analysis in the Journal of Quality Technology (1971, pp. 149155) reported the following data on y = ultimate shear...

The income statement, also known as the profit and loss (P&L) statement, provides a snapshot of the financial performance of a company during a specified period of time. It reports a firms gross...

Question 1 0 5 pts Eagle Industries' bonds have a 1 0 - year maturity and a 8 . 1 0 % coupon paid semiannually. They sell at their $ 1 , 0 0 0 par value, and are not callable. What is the effective...

The Landers Corporation needs to raise $1.90 million of debt on a 10-year issue. If it places the bonds privately, the interest rate will be 10 percent. Twenty five thousand dollars in out-of-pocket...