Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)259-304
Number of pages46
JournalJournal of Economic Theory
Volume54
Issue number2
DOIs
StatePublished - Aug 1991
Externally publishedYes

ASJC Scopus subject areas

  • Economics and Econometrics

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