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Relative growth optimal strategies in an asset market game

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  • Yaroslav Drokin
  • Mikhail Zhitlukhin

Abstract

We consider a game-theoretic model of a market where investors compete for payoffs yielded by several assets. The main result consists in a proof of the existence and uniqueness of a strategy, called relative growth optimal, such that the logarithm of the share of its wealth in the total wealth of the market is a submartingale for any strategies of the other investors. It is also shown that this strategy is asymptotically optimal in the sense that it achieves the maximal capital growth rate when compared to competing strategies. Based on the results obtained, we study the asymptotic structure of the market when all the investors use the relative growth optimal strategy.

Suggested Citation

  • Yaroslav Drokin & Mikhail Zhitlukhin, 2019. "Relative growth optimal strategies in an asset market game," Papers 1908.01171, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1908.01171
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    References listed on IDEAS

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    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    2. Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2017. "An Evolutionary Finance Model with a Risk-Free Asset," Swiss Finance Institute Research Paper Series 17-28, Swiss Finance Institute.
    3. Thomas Holtfort, 2019. "From standard to evolutionary finance: a literature survey," Management Review Quarterly, Springer, vol. 69(2), pages 207-232, June.
    4. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    5. Rabah Amir & Igor Evstigneev & Klaus Schenk-Hoppé, 2013. "Asset market games of survival: a synthesis of evolutionary and dynamic games," Annals of Finance, Springer, vol. 9(2), pages 121-144, May.
    6. 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.
    7. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    8. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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    Cited by:

    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. "Asymptotically optimal strategies in a diffusion approximation of a repeated betting game," Papers 2108.11998, arXiv.org.
    3. Mikhail Zhitlukhin, 2020. "Asymptotic minimization of expected time to reach a large wealth level in an asset market game," Papers 2007.04909, arXiv.org.
    4. Mikhail Zhitlukhin, 2020. "A continuous-time asset market game with short-lived assets," Papers 2008.13230, arXiv.org.
    5. Mikhail Zhitlukhin, 2021. "Capital growth and survival strategies in a market with endogenous prices," Papers 2101.09777, arXiv.org.

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