IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2873-d1180230.html
   My bibliography  Save this article

Optimal Investment of Merton Model for Multiple Investors with Frictions

Author

Listed:
  • Souhail Chebbi

    (Research Chair of Financial and Actuarial Studies, Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Senda Ounaies

    (Centre d’économie de la Sorbonne, Université Paris 1, Panthéon Sorbonne, 106–112 Boulevard de l’Hôpital, CEDEX 13, 75647 Paris, France)

Abstract

We investigate the classical optimal investment problem of the Merton model in a discrete time with market friction due to loss of wealth in trading. We consider the case of a finite number of investors, with the friction for each investor represented by a convex penalty function. This model cover the transaction costs and liquidity models studied previously in the literature. We suppose that each investor maximizes their utility function over all controls that keep the value of the portfolio after liquidation non-negative. In the main results of this paper, we prove the existence of an optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model via constructing a truncated economy, and the optimal strategy is obtained using a classical argument of limits.

Suggested Citation

  • Souhail Chebbi & Senda Ounaies, 2023. "Optimal Investment of Merton Model for Multiple Investors with Frictions," Mathematics, MDPI, vol. 11(13), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2873-:d:1180230
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2873/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2873/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    2. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-Based Models," Risks, MDPI, vol. 9(6), pages 1-13, June.
    3. repec:dau:papers:123456789/5630 is not listed on IDEAS
    4. Senda Ounaies & Jean-Marc Bonnisseau & Souhail Chebbi & Mete H. Soner, 2016. "Merton problem in an infinite horizon and a discrete time with frictions," PSE-Ecole d'économie de Paris (Postprint) halshs-01395604, HAL.
    5. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    6. repec:dau:papers:123456789/13605 is not listed on IDEAS
    7. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    8. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short‐Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232, July.
    9. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-based Models," Papers 2104.02694, arXiv.org, revised May 2021.
    10. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29, January.
    11. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    12. repec:dau:papers:123456789/5647 is not listed on IDEAS
    13. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    14. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    15. repec:dau:papers:123456789/416 is not listed on IDEAS
    16. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    17. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    18. Dumas, Bernard & Luciano, Elisa, 1991. "An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Francesca Mariani & Maria Cristina Recchioni & Tai-Ho Wang & Roberto Giacalone, 2024. "Can market volumes reveal traders' rationality and a new risk premium?," Papers 2406.05854, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    2. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    3. Dai, Min & Wang, Hefei & Yang, Zhou, 2012. "Leverage management in a bull–bear switching market," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1585-1599.
    4. Chellathurai, Thamayanthi & Draviam, Thangaraj, 2007. "Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2168-2195, July.
    5. repec:dau:papers:123456789/5374 is not listed on IDEAS
    6. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.
    7. Michal Czerwonko & Stylianos Perrakis, 2016. "Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics I: A Numerical Solution," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-23, December.
    8. Yingting Miao & Qiang Zhang, 2023. "Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility," Papers 2304.07672, arXiv.org.
    9. Xinfu Chen & Min Dai & Wei Jiang & Cong Qin, 2022. "Asymptotic analysis of long‐term investment with two illiquid and correlated assets," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1133-1169, October.
    10. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    11. Collin-Dufresne, Pierre & Daniel, Kent & Sağlam, Mehmet, 2020. "Liquidity regimes and optimal dynamic asset allocation," Journal of Financial Economics, Elsevier, vol. 136(2), pages 379-406.
    12. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    13. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    14. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.
    15. Changhui Choi & Bong-Gyu Jang & Changki Kim & Sang-youn Roh, 2016. "Net Contribution, Liquidity, and Optimal Pension Management," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 913-948, December.
    16. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "Optimal consumption and investment under transaction costs," Papers 1612.00720, arXiv.org.
    17. Jouini, Elyes & Kallal, Hedi, 2001. "Efficient Trading Strategies in the Presence of Market Frictions," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 343-369.
    18. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330, arXiv.org.
    19. Florent Gallien & Serge Kassibrakis & Semyon Malamud, 2018. "Hedge or Rebalance: Optimal Risk Management with Transaction Costs," Risks, MDPI, vol. 6(4), pages 1-14, October.
    20. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    21. Erindi Allaj, 2017. "Implicit Transaction Costs And The Fundamental Theorems Of Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-39, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2873-:d:1180230. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.