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Title: Optimal consumption under habit formation in markets with transaction costs and random endowments
Authors: Yu, X 
Issue Date: Apr-2017
Source: Annals of applied probability, Apr. 2017, v. 27, no. 2, p. 960-1002
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 multi asset 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.
Keywords: Proportional transaction costs
Unbounded random endowments
Acceptable portfolios
Consumption budget constraint
Consumption habit formation
Convex duality
Market isomorphism
Publisher: Institute of Mathematical Statistics
Journal: Annals of applied probability 
ISSN: 1050-5164
DOI: 10.1214/16-AAP1222
Rights: © Institute of Mathematical Statistics, 2017
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