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Portfolio Optimization with Different Information Flow recalls the stochastic tools and results concerning the stochastic optimization theory and the enlargement filtration theory. The authors detail a default free market and explore a defaultable market where the risks assets are subjected to the default risk of a counterparty firm, analyzing ways their value may suffer a sudden loss at the counterparty default time. Provides an overview of the role and impact of different information flow in the classical problem of optimal investmentExplores both a default free market and a defaultable market