Question: a let mt be a martingale under a probability measure...

(a) Let (Mt) 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 = Mt + g(t) a martingale under Q? Justify your argument.

(b) Let βt = e^(rt) be the value of the savings account at time t. Consider the model for the stock price

St = Xt + 0.1e^(sin(t)) where (Xt) solves the Black-Scholes SDE

that (St/βt) is not a martingale under Q.