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Unformatted text preview: IEOR 4106: Introduction to Operations Research: Stochastic Models Spring 2007, Professor Whitt, Final Exam Chapters 47 and 10 in Ross, Wednesday, May 9, 1:10pm4:00pm 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 HalasaYildirim Consulting Company Goes Public! (25 points) Ranwa Halasa and Burcu Yildirim have been so successful with their HalasaYildirim 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.
 Spring '08
 Staff
 Operations Research

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