We know a closed form solution of =adt + bdWe, for a, b E R is Y₁ Y Yo exp ((a-b²/2) t+bW₁) =

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We know a closed form solution of
Y₁
=adt + bdW₁, for a, b € R is
Y = Yo exp ((a - b²/2) t+bW₂)
where Yo is Y, at time t = 0. Using the probability density for ~ N (0, 1) show that the expected value
of Y, at time t > 0, given Yo, is
E[Ye Yo] = Yoet
Transcribed Image Text:We know a closed form solution of Y₁ =adt + bdW₁, for a, b € R is Y = Yo exp ((a - b²/2) t+bW₂) where Yo is Y, at time t = 0. Using the probability density for ~ N (0, 1) show that the expected value of Y, at time t > 0, given Yo, is E[Ye Yo] = Yoet
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