This problem is from a course called Derivatives & Risk Management, which is a graduate finance course in the MSc in Economics - Finance. I really hope for any kind of explanation/answer as to how to solve it, as i am in doubt about how to take this problem on. Thank you very much in advance!

Problem 3 Assume the process S follows a geometric Brownian motion, where z is a standard Brownian motion. a) Use lto's lemma to find the process followed by: In each case, express the coefficients of dt and dz in terms of Y rather than S. b) Could you also apply lto's lemma in a) if S would not follow a geometric Brownian motion? Explain your answer c) Briefly explain the main intuition for the derivation of the Black-Scholes-Merton differential equation. Which role does Ito's lemma play in it? Problem 3 Assume the process S follows a geometric Brownian motion, where z is a standard Brownian motion. a) Use lto's lemma to find the process followed by: In each case, express the coefficients of dt and dz in terms of Y rather than S. b) Could you also apply lto's lemma in a) if S would not follow a geometric Brownian motion? Explain your answer c) Briefly explain the main intuition for the derivation of the Black-Scholes-Merton differential equation. Which role does Ito's lemma play in it