Final09 - P u- identity 3 = -.5 .25 .25 .25 -.5 .25 .25 .25...

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Exercise 9 Today's stock price in the Acme Paint Company in dollars can be S := 10 20 30 based on yesterday's price. There is a p := 0.5 probability that the price of the stock today will be the same as yesterday. If the price changes, there is an equal probability that it will be either price. (a) Determine the transition probability matrix. P := p 1 - p 2 1 - p 2 1 - p 2 p 1 - p 2 1 - p 2 1 - p 2 p = .5 .25 .25 .25 .5 .25 .25 .25 .5
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(b) What is the average price of the stock? Π := Π 1 Π 2 Π 3 Π u P = Π Π 1 + Π 2 + Π 3 = 1 A :=
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Unformatted text preview: P u- identity 3 = -.5 .25 .25 .25 -.5 .25 .25 .25 -.5 A 3, 1 := 1 A 3, 2 := 1 A 3, 3 := 1 A = -.5 .25 .25 .25 -.5 .25 1 1 1 b := 1 Π := -1 A ⋅ b = 1 3 1 3 1 3 C := S ⋅Π = 20 (c) If you bought the stock when the price was $20, on the average, how long might you be able to wait to sell it when the price first reaches $30? Because the price cannot go higher than $30, one should sell it immediately. t := 0 ⋅ _day...
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This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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Final09 - P u- identity 3 = -.5 .25 .25 .25 -.5 .25 .25 .25...

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