Optimal consumption policies in illiquid markets
AbstractWe 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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Date of creation: 02 Jul 2008
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Illiquid market; optimal consumption; integrodifferential equations; viscosity solutions; semiconcavity; sub(super) differentials; optimal control;
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-07-14 (All new papers)
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- Huy�n 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.
- 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.
- Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2012. "Impact of time illiquidity in a mixed market without full observation," Papers 1211.1285, arXiv.org.
- Paul Gassiat & Fausto Gozzi & Huy\^en Pham, 2011.
"Investment/consumption problem in illiquid markets with regime-switching,"
1107.4210, arXiv.org, revised Apr 2012.
- Paul Gassiat & Fausto Gozzi & Huyen Pham, 2011. "Investment/consumption problem in illiquid markets with regimes switching," Working Papers hal-00610214, HAL.
- Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
- 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.
- 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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