Question: (b) W = W(t) is standard Brownian motion. Let f(S, t) be a function of two variables (continuously twice differentiable in S and once in

(b) W = W(t) is standard Brownian motion. Let f(S, t) be a function of two variables (continuously twice differentiable in S and once in t) obeying the stochastic differential equation: dS = udt + odw (i) Find an expression for I ( k ) = (W (t )) kaw(t ) that does not involve Ito integrals. (ii) Calculate the mean and variance of I(1). You may use without proof the fact that EW (T) 4] = 372. (iii) Evaluate d(exp[S(t) - t/2])

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