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The change in a share price satisfies dS=A(S,t)dX+B(S,t)dt. for some functions A, B what is the stochastic differential equation satisfied by f(S,t)? Can A, B

The change in a share price satisfies dS=A(S,t)dX+B(S,t)dt. for some functions A, B what is the stochastic differential equation satisfied by f(S,t)? Can A, B be chosen so that a function g(S) has zero drift, but non-zero varience?

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