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Liquidation of an indivisible asset with independent investment

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  • Emilie Fabre
  • Guillaume Royer
  • Nizar Touzi

Abstract

We provide an extension of the explicit solution of a mixed optimal stopping-optimal stochastic control problem introduced by Henderson and Hobson. The problem examines wether the optimal investment problem on a local martingale financial market is affected by the optimal liquidation of an independent indivisible asset. The indivisible asset process is defined by a homogeneous scalar stochastic differential equation, and the investor's preferences are defined by a general expected utility function. The value function is obtained in explicit form, and we prove the existence of an optimal stopping-investment strategy characterized as the limit of an explicit maximizing strategy. Our approach is based on the standard dynamic programming approach.

Suggested Citation

  • Emilie Fabre & Guillaume Royer & Nizar Touzi, 2013. "Liquidation of an indivisible asset with independent investment," Papers 1312.2754, arXiv.org, revised Feb 2015.
    • Handle: RePEc:arx:papers:1312.2754
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    References listed on IDEAS

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    1. Vicky Henderson & David Hobson, 2008. "An explicit solution for an optimal stopping/optimal control problem which models an asset sale," Papers 0806.4061, arXiv.org, revised Nov 2008.
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