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### Solutions to Problems to Work for Understanding

What is the solution of the stochastic differential equation
dY(t) = \mu(t) Y(t) dt + \sigma Y(t) dX
Note the difference with the previous problem, now \mu(t) is a general, bounded integrable function of time. This problem is adapted from Financial Calculus: An introduction to derivative pricing by M Baxter, and A. Rennie, Cambridge University Press, 1996, page 61, Exercise 3.5 We could match both the drift and volaility terms for this SDE to the known SDE for the process \exp(\rho X(t) + \nu(t) t) if and only if we take \sigma = \rho and \vu = \mu - (1/2)\sigma^2. That is, we guess the solution of the SDE to be
Y(t) = \exp( \sigma X(t) + (\int_0^t \mu(s) ds - (1/2) \sigma^2)t)
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