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

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  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!

 

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