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Let Q be a probability measure that is equivalent to P, that is Q( omega ) > 0 for all omega ohm Set XT( omega
Let Q be a probability measure that is equivalent to P, that is Q( omega ) > 0 for all omega ohm Set XT( omega ) = Q( omega )/P( omega ), and let Xt = [XT|Ft|, t = 0, 1, . . . , T - 1. Show that X is a strictly positive process with X0 = 1. Let { Yt : t = 0,1, . . . ,T} be a stochastic process. Show that Y is a martingale under Q if and only if the process {XtYt : t = 0,1, . . . ,T} is a martingale under P. Let Q be a probability measure that is equivalent to P, that is Q( omega ) > 0 for all omega ohm Set XT( omega ) = Q( omega )/P( omega ), and let Xt = [XT|Ft|, t = 0, 1, . . . , T - 1. Show that X is a strictly positive process with X0 = 1. Let { Yt : t = 0,1, . . . ,T} be a stochastic process. Show that Y is a martingale under Q if and only if the process {XtYt : t = 0,1, . . . ,T} is a martingale under P
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