Optimal investment with random endowments and transaction costs: duality theory and shadow prices

Erhan Bayraktar, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

This paper studies the utility maximization on the terminal wealth with random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistent price system such that the liquidation value processes stay above some stochastic thresholds. In the market consisting of one riskless bond and one risky asset, we obtain a type of super-hedging result. Based on this characterization of the primal space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the duality approach. As an important application of the duality theorem, we provide some sufficient conditions for the existence of a shadow price process with random endowments in a generalized form similar to Czichowsky and Schachermayer (Ann Appl Probab 26(3):1888–1941, 2016) as well as in the usual sense using acceptable portfolios.

Original languageEnglish
Pages (from-to)253-286
Number of pages34
JournalMathematics and Financial Economics
Volume13
Issue number2
DOIs
Publication statusPublished - 1 Mar 2019

Keywords

  • Acceptable portfolios
  • Convex duality
  • Proportional transaction costs
  • Shadow prices
  • Unbounded random endowments
  • Utility maximization

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

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