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On the existence of shadow prices for optimal investment with random endowment

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  • Lingqi Gu
  • Yiqing Lin
  • Junjian Yang

Abstract

In this paper, we consider a num\'eraire-based utility maximization problem under constant proportional transaction costs and random endowment. Assuming that the agent cannot short sell assets and is endowed with a strictly positive contingent claim, a primal optimizer of this utility maximization problem exists. Moreover, we observe that the original market with transaction costs can be replaced by a frictionless shadow market that yields the same optimality. On the other hand, we present an example to show that in some case when these constraints are relaxed, the existence of shadow prices is still warranted.

Suggested Citation

  • Lingqi Gu & Yiqing Lin & Junjian Yang, 2016. "On the existence of shadow prices for optimal investment with random endowment," Papers 1602.01109, arXiv.org, revised Feb 2017.
    • Handle: RePEc:arx:papers:1602.01109
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    References listed on IDEAS

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    Cited by:

    1. Miklos Rasonyi, 2017. "On utility maximization without passing by the dual problem," Papers 1702.00982, arXiv.org, revised Mar 2018.

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