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3. a let mt be a martingale under a probability measure...

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

###### Question details

1. (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.

2.
3. (b)  Let βt = ert be the value of the savings account at time t. Consider the model for the stock price

St = Xt + 0.1esin(t) where (Xt) solves the Black-Scholes SDE

dX= rXtdt + σXtd(Bt_hat)X = 1

Here (Bt_hat) is a Brownian motion under Q which turns (Xtt) into a martingale. Show that (Stt) is NOT a martingale under Q.

Hint: The result of part a will help!