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1. Consider a stock and assume it follows a geometric Brownian motion dS = dt+dz. Consider now a function G = G(S, t). i) Use

1. Consider a stock and assume it follows a geometric Brownian motion dS = dt+dz. Consider now a function G = G(S, t).

i) Use Itos lemma to find the stochastic process dG followed by G^2.

ii) Show that this value satisfies the Black-Scholes-Merton Partial Differential Equation :

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