Question: Question 3 [12 marks] Consider the processes X, = (1 + #2(m + B), Y, = exp(X), t2 0, where m 6 R and B,

Question 3 [12 marks] Consider the processes X, = (1 + #2(m + B), Y, = exp(X), t2 0, where m 6 R and B, is a standard Brownian motion. (a) Evaluate EX - XX = x alt, x) =Him h to find the drift coefficient of X, [3 marks]. (b) Derive the transition density of X, [3 marks]. (c) Find the Ito representation of X, [3 marks]. (d) Find the Ito representation of Y, [3 marks]

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