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Merton problem in an infinite horizon and a discrete time with frictions

Author

Listed:
  • Senda Ounaies

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Marc Bonnisseau

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Souhail Chebbi

    (KSU - King Saud University [Riyadh])

  • Mete H. Soner

    (D-MATH - Department of Mathematics [ETH Zurich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich])

Abstract

We investigate the problem of optimal investment and consumption of Merton in the case of discrete markets in an infinite horizon. We suppose that there is frictions in the markets due to loss in trading. These frictions are modeled through nonlinear penalty functions and the classical transaction cost and liquidity models are included in this formulation. In this context, the solvency region is defined taking into account this penalty function and every investigator have to maximize his utility, that is derived from consumption, in this region. We give the dynamic programming of the model and we prove the existence and uniqueness of the value function.

Suggested Citation

  • Senda Ounaies & Jean-Marc Bonnisseau & Souhail Chebbi & Mete H. Soner, 2016. "Merton problem in an infinite horizon and a discrete time with frictions," Post-Print halshs-01395604, HAL.
    • Handle: RePEc:hal:journl:halshs-01395604
    DOI: 10.3934/jimo.2016.12.1323
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    Cited by:

    1. Xue Dong He & Chen Yang & Yutian Zhou, 2024. "Liquidity Pool Design on Automated Market Makers," Papers 2404.13291, arXiv.org.
    2. Souhail Chebbi & Senda Ounaies, 2023. "Optimal Investment of Merton Model for Multiple Investors with Frictions," Mathematics, MDPI, vol. 11(13), pages 1-10, June.

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