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Let $ (\Omega,\mathbb P)$ be a probability space supporting independent random variables $ U_n,n=1,2,\cdots,N$ and $ V$ . Let the filtration be given by $ \mathcal F_n=\mathcal F_n^{U,V}$ . Consider the following optimization problem $ $ \mathbb E (\sum_{n=1}^NU_n P_n)\rightarrow \max $ $ where the maximization is taken over all martingale of the form $Read more