Optimal consumption under habit formation in markets with transaction costs and random endowments

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4 Citations (Scopus)

Abstract

This paper studies the optimal consumption via the habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multiasset framework with a cash account. At the terminal time T , the investor can receive unbounded random endowments for which we propose a new definition of acceptable portfolios based on the strictly consistent price system (SCPS).We prove a type of super-hedging theorem using the acceptable portfolios which enables us to obtain the consumption budget constraint condition under market frictions. Following similar ideas in [Ann. Appl. Probab. 25 (2015) 1383-1419] with the path dependence reduction and the embedding approach, we obtain the existence and uniqueness of the optimal consumption using some auxiliary processes and the duality analysis. As an application of the duality theory, the market isomorphism with special discounting factors is also discussed in the sense that the original optimal consumption with habit formation is equivalent to the standard optimal consumption problem without the habits impact, however, in a modified isomorphic market model.
Original languageEnglish
Pages (from-to)960-1002
Number of pages43
JournalAnnals of Applied Probability
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • Acceptable portfolios
  • Consumption budget constraint
  • Consumption habit formation
  • Convex duality
  • Market isomorphism
  • Proportional transaction costs
  • Unbounded random endowments

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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