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Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1

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  • Hua He
  • Neil D. Pearson

Abstract

We use a martingale approach to study optimal intertemporal consumption and portfolio policies in a general discrete‐time, discrete‐state‐space securities market with dynamically incomplete markets and short‐sale constraints. We characterize the set of feasible consumption bundles as the budget‐feasible set defined by constraints formed using the extreme points of the closure of the set of Arrow‐Debreu state prices consistent with no arbitrage, and then establish a relationship between the original problem and a dual minimization problem.

Suggested Citation

  • Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10, July.
    • Handle: RePEc:bla:mathfi:v:1:y:1991:i:3:p:1-10
    DOI: 10.1111/j.1467-9965.1991.tb00012.x
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    References listed on IDEAS

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    1. Grossman, Sanford J. & Vila, Jean-Luc, 1992. "Optimal Dynamic Trading with Leverage Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 151-168, June.
    2. Cox, John C. & Huang, Chi-fu., 1989. "A variational problem arising in financial economics," Working papers 2110-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
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