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Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case. (English) Zbl 0736.90017
Summary: We employ a martingale approach to study a dynamic consumption-portfolio problem in continuous time with incomplete markets and short-sale constraints. We introduce a notion of minimax local martingale and transform the dynamic problem into a static problem of maximizing expected utility over the consumption bundles that satisfy a single budget constraint formed using that measure. We establish the existence of and characterize the minimax local measure, provide sufficient conditions for the dynamic consumption-portfolio problem to have a solution, and relate the optimal policies to the solution of quasi-linear partial differential equation.

MSC:
91B62 Economic growth models
91B28 Finance etc. (MSC2000)
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