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Optimal consumption policies in illiquid markets

Author

Listed:
  • Alessandra Cretarola

    ()

  • Fausto Gozzi

    ()

  • Huyên Pham

    ()

  • Peter Tankov

    ()

Abstract

We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.
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Suggested Citation

  • Alessandra Cretarola & Fausto Gozzi & Huyên Pham & Peter Tankov, 2011. "Optimal consumption policies in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 85-115, January.
  • Handle: RePEc:spr:finsto:v:15:y:2011:i:1:p:85-115
    DOI: 10.1007/s00780-010-0123-y
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    File URL: http://hdl.handle.net/10.1007/s00780-010-0123-y
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    References listed on IDEAS

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    1. 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.
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    Citations

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    Cited by:

    1. Paul Gassiat & Fausto Gozzi & Huy^en Pham, 2011. "Investment/consumption problem in illiquid markets with regime-switching," Papers 1107.4210, arXiv.org, revised Apr 2012.
    2. Paul Gassiat & Huyen Pham & Mihai Sirbu, 2009. "Optimal investment on finite horizon with random discrete order flow in illiquid markets," Papers 0907.2203, arXiv.org.
    3. Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
    4. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2017. "Impact Of Time Illiquidity In A Mixed Market Without Full Observation," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 401-437, April.
    5. Stefano Baccarin, 2013. "Optimal Consumption of a Generalized Geometric Brownian Motion with Fixed and Variable Intervention Costs," Working papers 021, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    6. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    7. Castellano, Rosella & Cerqueti, Roy, 2014. "Mean–Variance portfolio selection in presence of infrequently traded stocks," European Journal of Operational Research, Elsevier, vol. 234(2), pages 442-449.

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