This paper studies the utility maximization problem on consumption with addictive habit formation in the market with proportional transaction costs and unbounded random endowment . To model the proportional transaction costs, we adopt the Kabanov's multi-asset framework with a cash account. At the terminal time t= T, the investor can receive an unbounded random endowment for which we propose a new definition of acceptable portfolio processes depending on the strictly consistent price system (SCPS). We prove a type of super-hedging theorem for a family of workable contingent claims using the acceptable portfolios and random endowment which enables us to obtain the consumption budget constraint result under the market frictions. With the path dependence reduction and the embedding approach, the existence and uniqueness of the optimal consumption are proved using the auxiliary primal and dual processes and the convex duality analysis .
This paper studies the optimal consumption under the addictive 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. Applying the path dependence reduction and the embedding approach, the existence and uniqueness of the optimal consumption are obtained using some auxiliary processes and the duality approach. 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 habits impact, however, in a modified isomorphic market model .
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utility maximization problem on consumption with
optimal consumption under the
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in the market with proportional
preference in markets with
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endowment
endowments
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t=
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an unbounded random endowment
unbounded random endowments
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portfolio processes depending
portfolios based
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for a family of workable contingent claims
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and random endowment
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result under the
condition under
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With
Applying
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proved using the auxiliary primal and dual
obtained using some auxiliary
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convex duality analysis
duality approach. 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 habits impact, however, in a modified isomorphic market model