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Viscosity characterization of the value function of an investment-consumption problem in presence of illiquid assets

  • Salvatore Federico
  • Paul Gassiat

We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded and observed at discrete random times corresponding to the jumps of a Poisson process. The problem is a nonstandard mixed discrete/continuous optimal control problem which we face by the dynamic programming approach. The main aim of the paper is to prove that the value function is the unique viscosity solution of an associated HJB equation. We then use such result to build a numerical algorithm allowing to approximate the value function and so to measure the cost of illiquidity.

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File URL: http://arxiv.org/pdf/1211.1286
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Paper provided by arXiv.org in its series Papers with number 1211.1286.

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Date of creation: Nov 2012
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Handle: RePEc:arx:papers:1211.1286
Contact details of provider: Web page: http://arxiv.org/

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  1. Eduardo S. Schwartz & Claudio Tebaldi, 2006. "Illiquid Assets and Optimal Portfolio Choice," NBER Working Papers 12633, National Bureau of Economic Research, Inc.
  2. Paul Gassiat & Fausto Gozzi & Huyen Pham, 2011. "Investment/consumption problem in illiquid markets with regimes switching," Working Papers hal-00610214, HAL.
  3. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2012. "Impact of time illiquidity in a mixed market without full observation," Papers 1211.1285, arXiv.org, revised Mar 2015.
  4. Huyên Pham & Peter Tankov, 2008. "A Model Of Optimal Consumption Under Liquidity Risk With Random Trading Times," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 613-627.
  5. Andrew Ang & Dimitris Papanikolaou & Mark Westerfield, 2013. "Portfolio Choice with Illiquid Assets," NBER Working Papers 19436, National Bureau of Economic Research, Inc.
  6. Koichi Matsumoto, 2006. "Optimal portfolio of low liquid assets with a log-utility function," Finance and Stochastics, Springer, vol. 10(1), pages 121-145, 01.
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