2. Consider the geometric Brownian motion process S(t) = Soet+ow (t), as defined in Exercise 10.21, where ER, o > 0. For

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2 Consider The Geometric Brownian Motion Process S T Soet Ow T As Defined In Exercise 10 21 Where Er O 0 For 1 (37.3 KiB) Viewed 34 times

2. Consider the geometric Brownian motion process S(t) = Soet+ow (t), as defined in Exercise 10.21, where ER, o > 0. For any time T > 0, and levels B < So, y < ∞, derive a formula for the conditional probability: P (m³ (T) > B|S(T) = y) inf_S(t). where m$(T): 0<t<T [Hint: You may relate this to a drifted BM and then use an appropriate conditioning that makes use of the joint density of the minimum and the drifted BM value at time T. Also note that for any two continuous r.v.'s X, Y we have P (YE (a, b) | X = x) = f fyx (y|x) dy.]