Question: dS(t)=rS(t)dt+S(t)dW(t) where r and >0 are constant and W(t) is a Brownian motion under the risk- neutral measure P. Consider a derivative security that pays

dS(t)=rS(t)dt+S(t)dW(t) where r and >0 are constant and W(t) is a Brownian motion under the risk- neutral measure P. Consider a derivative security that pays S2(t) at time T. Construct a portfolio that trades in the stock and a money market account with constant rate of interest r so that the final value of the portfolio X(T) is S2(T) almost surely. In particular, specify what X(0) should be, and how many shares of stock (t) the portfolio should hold at each time t

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