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2010 Q1ii)

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xdorax

Member
How do you know where to start when solving SDE question?
in this case, why Let Xt = Ut exp (-gamma t) ?

Thanks
 
The general form of dX(t) = -gamma * X(t) * dt has solution: constant * exp[-gamma * t], so the answer makes an educated guess as to the form of the solution for the equation in question.

It's explained in a bit more detail in the section on the Ornstein-Uhlenbeck process in the stochastic calculus chapter. You could also look on wikipedia for "examples of differential equations" to find more info on solving them (I've brushed up a bit today).
 
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