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We study regularity properties of the dynamic value functions of primal anddual problems of optimal investing for utility functions defined on the wholereal line. Relations between decomposition terms of value processes of primaland dual problems and between optimal solutions of basic and conditionalutility maximization problems are established. These properties are used toshow that the value function satisfies a corresponding backward stochasticpartial differential equation.  In the case of complete markets we give conditions on the utility functionwhen this equation admits a solution.

On regularity of primal and dual dynamic value functions related to investment problem