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I lost in the steps so can someone clarify to me how to solve this following the steps? Problem 1 In this problem, you will
I lost in the steps so can someone clarify to me how to solve this following the steps?
Problem 1 In this problem, you will use the following steps to show that Var(J, CsdBs) = So E[Colds where Ct is adapted to the natural filtration associated with the Brownian motion Be: n 1. Consider the finite sum Sn = _ Cti,(Bt; - Bt:1) so that limn > Sn = So CsdBs. Show i= that n Var(Sn) = > Var(Cti-1 (Bti - Bti-1) ) i=1 2. Write Var(Cti-1 (Bt; - Bti-1)) = E[(Cti, (Bt; - Bti-1))"] - (E[Cti, (Bt; - Bti-1)])2 Use the law of iterated expectation to show that E[Cti , (Bt; - Bti-1)] = 0 and E[(Cti-, (Bti - Bti-1))?] = E[C?_](ti - ti-1). 3. Take the limit when n - co to conclude that Var(for CsdBs) = So E[C,]dsStep by Step Solution
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