finalS07 - IEOR 4106: Introduction to Operations Research:...

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Unformatted text preview: IEOR 4106: Introduction to Operations Research: Stochastic Models Spring 2007, Professor Whitt, Final Exam Chapters 4-7 and 10 in Ross, Wednesday, May 9, 1:10pm-4:00pm Open Book: but only the Ross textbook, the CTMC Notes, the class notes related to Chapters 7 and 10, and three 8 × 11 pages of notes Honor Code: Students are expected to behave honorably when taking exams. After completing the test, please testify to your adherence by writing the following on your bluebook and signing your name: “I have neither given nor received help while taking this test.” Justify your answers; show your work. 1. The Halasa-Yildirim Consulting Company Goes Public! (25 points) Ranwa Halasa and Burcu Yildirim have been so successful with their Halasa-Yildirim Con- sulting Company, that their company has gone public, and is now listed on the New York Stock Exchange under the HY symbol. Suppose that a share of HY stock initially costs $80 per share. Suppose that the HY stock share price over time (measured in years) is modelled as the stochastic process { X ( t ) : t ≥ } , where X ( t ) = 80 + 5 B ( t ) , t ≥ , with { B ( t ) : t ≥ } being standard Brownian motion, having E [ B ( t )] = 0 and V ar ( B ( t )) = t for t ≥ 0. (a) What is the probability that the HY stock price is greater than $100 after 2 years? (b) What is the conditional expected HY stock price after 1 year, given that the HY stock price is $130 per share after 5 years? (c) What is the approximate conditional probability that the HY stock price after 1 year exceeds 94 . 5, given that the HY stock price is $130 per share after 5 years? (Hint: √ 5 ≈ 2 . 24) (d) What is the probability that the HY stock price rises to $100 per share before it drops to $70 per share?...
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This note was uploaded on 04/25/2010 for the course IEOR 3106 taught by Professor Staff during the Spring '08 term at Columbia.

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finalS07 - IEOR 4106: Introduction to Operations Research:...

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