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17-05-07 - UF-ESI-6321.xmcd page 1 of 2 17.5.7 Consider two...

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UF-ESI-6321 17-05-07.xmcd page 1 of 2 17.5.7 Consider two stocks. Stock 1 always sells for $10 or $20. S 1 10 20 ( ) := If stock 1 is selling for $10 today, there is a .80 chance that it will sell for $10 tomorrow. If stock 1 is selling for $20 today, there is a .90 chance that it will sell for $20 tomorrow. Let matrix rows represent selling prices today and columns represent selling prices tomorrow with corresponding elements representing probabilities of price transitions from today to tomorrow: p 1 .80 .10 .20 .90 := π 1 π 2 ( ) p 1 T 0.8 π 1 0.1 π 2 + 0.2 π 1 0.9 π 2 + π 2 1 π 1 - = π 1 1 π 1 - ( ) p 1 T 0.7 π 1 0.1 + 0.7 - π 1 0.9 + Using a Mathcad solve block requires making an initial guess value: π 1 0.5 := Given π 1 1 π 1 - ( ) p 1 T π 1 1 π 1 - = π 1 Find π 1 ( ) := π 2 1 π 1 - := π 1 π 2 1 3 2 3 = Expected price of Stock 1 in dollars: P 1 S 1 π 1 π 2 16.67 = := Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435
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