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# Final09 - P u identity 3 =.5.25.25.25.5.25.25.25.5 A 3 1:=...

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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 uniE002 P = Π Π 1 + Π 2 + Π 3 = 1 A := P uniE002
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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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