Question: hi, i need help with qn2. Do provide email so i can send relevant references to you if needed! thank you! 2) Let (S )tefor

hi, i need help with qn2. Do provide email so i can send relevant references to you if needed! thank you!

2) Let (S )tefor be the solution of the stochastic differential equation dS= (1) VT -t with So > 0. a) (10 marks) Show that (So)co,T-] is a martingale on [0, T - =] for every & E (0, T). Hint: Solve the stochastic differential equation (1) by the method of Proposition 6.16-a), and use Exercise 5.11-b). b) (5 marks) Find the value of Sy by a simple argument. c) (10 marks) Show that (St)tejo,7 is a strict local martingale on [0, T']. Hint: Consider the stopping times Tn := ( (1 - #) T ) AimIft = 10, I] : 15:12n), 121, and use Proposition 8.1. d) (5 marks) Plot a sample graph of (Sthejo,7 with T = 1, and attach or upload it with your submission

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