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**:** 2015
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** (.):** arbitrage-free markets, incomplete markets, consumption problems,scenariotree,dynamicprogramming,convexprogramming

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** (.):** We consider a multi-period discrete model of an incomplete market evolving with respect to a non-recombining scenario tree. The investor maximizes expected utility of his of her consumption over a finite time horizon. Decomposition schemes are suggested for optimal consumption-investment problems with power-like and logarithmic utility functions. We introduce dynamic programming algorithms that reduce the original problem to the set of one-period problems.

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