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$$ Z_t = f(S_t) := \left( \frac{S_t}{H} \right)^p $$ $$ dZ_t = \partial_x f(S_t) dS_t + \frac{1}{2} \partial^2_{xx} f(S_t) d\langle S \rangle_t = p\frac{S_t^{p-1}}{H^p} dS_t + \frac{1}{2} p(p-1) \frac{S_t^{p-2}}{H^p} S_t^2 \sigma^2 dt $$ Thus $$ dZ_t = Z_t \left( p r + \frac{1}{2} p(p-1) \sigma^2 \right)dt + p Z_t \sigma dW_t $$ so that $$ \frac{dZ_t}{Z_t} = ...



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