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26. [3 points] Let B be a one-dimensional Brownian motion, and let S(0) be a positive constant. Let / be a non-random function of time
26. [3 points] Let B be a one-dimensional Brownian motion, and let S(0) be a positive constant. Let / be a non-random function of time that is locally integrable, meaning that it is a measurable function and for every t E 0, 0o) , In(s) | ds 0 be a constant. Let S be the stock price process given by S(t) = S(0)exp ( ( 4 - 302) as + OB() Given t E [0, oo), define Me = / Meds and Ut = 0't Find an expression for S(t) in terms of S(0), At, Ut, o and B(t), and then calculate the expectation of S(t)
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