Question: (a) Let (Me) be a martingale under a probability measure Q and let g be a deterministic function. Assume that g is not constant in

(a) Let (Me) be a martingale under a probability measure Q and let g be a deterministic function. Assume that g is not constant in t. Is the process Ut = Mc + g(t) a martingale under Q? Justify your argument. (b) Consider the following model. Let B, = e" be the value of the savings account at time t, and let the stock price (S,) be given by S, = Y, + 0.1esin(t) where (Y) solves the SDE dy, = rYdt +oVidBr, Yo =1. Here (B.) is a Brownian motion under Q. Is the process (St/8,) a martingale under Q? (c) Let P be the real world probability measure for this model. Additionally, assume that Q and P are equivalent probability measures. Is Q an EMM for this model? Justify your argument

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