Question: 4. Suppose dXt = (rtX+ + Ment) dt + medBt, Pt = exp ( (As - 203 ) ds+ Cs dBs). It is known that

4. Suppose dXt = (rtX+ + Ment) dt + medBt, Pt

4. Suppose dXt = (rtX+ + Ment) dt + medBt, Pt = exp ( (As - 203 ) ds+ Cs dBs). It is known that ptXt is a martingale for any Tit. (a) Show that dot = Pt(At dt + CtdB.) by Ito's Lemma. [7 marks] (b) Express At and Ct in terms of rt and fit. [5 marks] (c) Show that if XT > 0, then Xt > 0 for all t > 0. [3 marks]

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