IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2211.05316.html
   My bibliography  Save this paper

Optimal growth strategies for a representative agent in a continuous-time asset market

Author

Listed:
  • Mikhail Zhitlukhin

Abstract

We propose a multi-agent model of an asset market and study conditions that guarantee that the strategy of an individual agent cannot outperform the market. The model assumes a mean-field approximation of the market by considering an infinite number of infinitesimal agents who use the same strategy and another infinitesimal agent with a different strategy who tries to outperform the market. We show that the optimal strategy for the market agents is to split their investment budgets among the assets proportionally to their discounted expected relative dividend intensities.

Suggested Citation

  • Mikhail Zhitlukhin, 2022. "Optimal growth strategies for a representative agent in a continuous-time asset market," Papers 2211.05316, arXiv.org.
    • Handle: RePEc:arx:papers:2211.05316
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2211.05316
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    2. Thomas Holtfort, 2019. "From standard to evolutionary finance: a literature survey," Management Review Quarterly, Springer, vol. 69(2), pages 207-232, June.
    3. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
    4. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    5. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    6. Evstigneev, Igor & Hens, Thorsten & Potapova, Valeriya & Schenk-Hoppé, Klaus R., 2020. "Behavioral equilibrium and evolutionary dynamics in asset markets," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 121-135.
    7. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 74(4), pages 929-966, July.
    8. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    9. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    10. Constantinos Kardaras, 2008. "Balance, growth and diversity of financial markets," Papers 0803.1858, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    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. Mikhail Zhitlukhin, 2022. "A continuous-time asset market game with short-lived assets," Finance and Stochastics, Springer, vol. 26(3), pages 587-630, July.
    2. Mikhail Zhitlukhin, 2021. "Capital growth and survival strategies in a market with endogenous prices," Papers 2101.09777, arXiv.org.
    3. Hirshleifer, David & Lo, Andrew W. & Zhang, Ruixun, 2023. "Social contagion and the survival of diverse investment styles," Journal of Economic Dynamics and Control, Elsevier, vol. 154(C).
    4. Zeckhauser, Richard Jay & Tran, Ngoc-Khanh, 2011. "The Behavior of Savings and Asset Prices When Preferences and Beliefs are Heterogeneous," Scholarly Articles 5027955, Harvard Kennedy School of Government.
    5. Ani Guerdjikova & John Quiggin, 2018. "Intertemporal Portfolio Choice with Incorrect Beliefs and Aversion to Surprise," Post-Print hal-02086151, HAL.
    6. Peter A. F. Fraser‐Mackenzie & Tiejun Ma & Ming‐Chien Sung & Johnnie E. V. Johnson, 2019. "Let's Call it Quits: Break‐Even Effects in the Decision to Stop Taking Risks," Risk Analysis, John Wiley & Sons, vol. 39(7), pages 1560-1581, July.
    7. Andrew W. Lo & H. Allen Orr & Ruixun Zhang, 2018. "The growth of relative wealth and the Kelly criterion," Journal of Bioeconomics, Springer, vol. 20(1), pages 49-67, April.
    8. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2019. "Momentum and reversal in financial markets with persistent heterogeneity," Annals of Finance, Springer, vol. 15(4), pages 455-487, December.
    9. Kogan, Leonid & Ross, Stephen A. & Wang, Jiang & Westerfield, Mark M., 2017. "Market selection," Journal of Economic Theory, Elsevier, vol. 168(C), pages 209-236.
    10. Massari, Filippo, 2019. "Market selection in large economies: a matter of luck," Theoretical Economics, Econometric Society, vol. 14(2), May.
    11. Jaroslav Borovička, 2020. "Survival and Long-Run Dynamics with Heterogeneous Beliefs under Recursive Preferences," Journal of Political Economy, University of Chicago Press, vol. 128(1), pages 206-251.
    12. Yaroslav Drokin & Mikhail Zhitlukhin, 2020. "Relative growth optimal strategies in an asset market game," Annals of Finance, Springer, vol. 16(4), pages 529-546, December.
    13. Ani Guerdjikova & John Quiggin, 2018. "Heuristic Modes of Decision Making and Survival in Financial Markets," Post-Print hal-02086078, HAL.
    14. Sihvonen, Markus, 2019. "Market selection with idiosyncratic uncertainty," Journal of Economic Theory, Elsevier, vol. 182(C), pages 143-160.
    15. Dindo, Pietro, 2019. "Survival in speculative markets," Journal of Economic Theory, Elsevier, vol. 181(C), pages 1-43.
    16. He, Xue-Zhong & Shi, Lei, 2017. "Index portfolio and welfare analysis under heterogeneous beliefs," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 64-79.
    17. Guerdjikova, Ani & Sciubba, Emanuela, 2015. "Survival with ambiguity," Journal of Economic Theory, Elsevier, vol. 155(C), pages 50-94.
    18. ÅžimÅŸek, Alp, 2021. "The Macroeconomics of Financial Speculation," CEPR Discussion Papers 15733, C.E.P.R. Discussion Papers.
    19. Elyès Jouini & Clotilde Napp, 2010. "Unbiased Disagreement in Financial Markets, Waves of Pessimism and the Risk-Return Trade-off," Review of Finance, European Finance Association, vol. 15(3), pages 575-601.
    20. Pohl, Walter & Schmedders, Karl & Wilms, Ole, 2021. "Asset pricing with heterogeneous agents and long-run risk," Journal of Financial Economics, Elsevier, vol. 140(3), pages 941-964.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2211.05316. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.