Past exam of the martingales and financial mathematics course of the University of Oxford / 2011 / B / 5 / d / Solution

Apply Itô's formula to $V_t=A(t)S_t^3$, where $A^{\prime }(t)=-(2r+3{\sigma }^2)A(t)$. Since $d{S}_t/S_t=\mu dt+\sigma d{W}_3(t)$, the drift and diffusion areThusUnder the risk-neutral measure its drift becomes $3r-2r=r$, as required for a traded, non-dividend-paying replicating asset.