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CM2 Acted notes page 40 – q 10.5 (iii)

Discussion in 'CM2' started by bobby sanger, Mar 29, 2020.

  1. bobby sanger

    bobby sanger Member

    CM2 Acted notes page 40 – q 10.5 (iii)


    Answer states:

    Mu = 0 and sigma = 0.

    Using equation from part (i), we require

    g'(t)Bt + ½*6Bt = 0


    Which equation are we using from part (i) to form g'(t)Bt + ½*6Bt = 0 and what are the steps involved to get to this point?

    best wishes

    bobby
     
    bobby sanger, Mar 29, 2020
    #1
  2. Joe Hook

    Joe Hook ActEd Tutor Staff Member

    Hi Bobby,

    So we're using the final equation of part (i), the one that following "For a martingale we require zero drift and hence".

    With g(t) a function of time our overall expression here: Bt^3 +g(t)Bt is itself a function of both time and standard Brownian motion. With mu=0 and sigma=1 we can take the first partial differential of Bt^3 + g(t)Bt with respect to t and the second partial derivative with respect to Bt and plug into our equation from part (i).

    Hopefully this gets you there.
    Let me know if any issues remain unsolved.
    Joe
     
    Joe Hook, Apr 22, 2020
    #2

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