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I'm not sure what this question is asking me to do. Any guidance would be much appreciated! This is the question in its entirety. 7.
I'm not sure what this question is asking me to do. Any guidance would be much appreciated!
This is the question in its entirety.
7. (10%) (a) (2%; 2%) If Z=S*eMT-6 and dS=uSdt+oSdB, we know dz=m, Zdt+n, ZdB using Ito's formula (lemma). Find the values of m, and ni. (Hint: You can refer to page 312 of the textbook or the lecture note.) (b) (3%; 3%) If Z=e* and dX = (-1/2)*o?dt+odB, we know dz=m2Zdt+n22dB using Ito's formula (lemma). Find the values of me and nu. Note 1: Ito's formula: If Z(t)=g(t, X(t)), where dX(t) = uzdt+0xdB dx)2=0 dt then dZ = (@g/@t)*dt + (@g/@x)*dX + 1/2*(@g/@x)*(dx)? Note 2: [@(S*eMT+}}/@t] = [S*eT**]*[@r(T-ty/@t] =-rSeT); (@e*/@x)=eX 7. (10%) (a) (2%; 2%) If Z=S*eMT-6 and dS=uSdt+oSdB, we know dz=m, Zdt+n, ZdB using Ito's formula (lemma). Find the values of m, and ni. (Hint: You can refer to page 312 of the textbook or the lecture note.) (b) (3%; 3%) If Z=e* and dX = (-1/2)*o?dt+odB, we know dz=m2Zdt+n22dB using Ito's formula (lemma). Find the values of me and nu. Note 1: Ito's formula: If Z(t)=g(t, X(t)), where dX(t) = uzdt+0xdB dx)2=0 dt then dZ = (@g/@t)*dt + (@g/@x)*dX + 1/2*(@g/@x)*(dx)? Note 2: [@(S*eMT+}}/@t] = [S*eT**]*[@r(T-ty/@t] =-rSeT); (@e*/@x)=eX Step by Step Solution
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