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A continuous-time asset market game with short-lived assets

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  • Mikhail Zhitlukhin

Abstract

We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors and to provide conditions for the existence of its solution. The second goal is to show that there exists a strategy such that the logarithm of the relative wealth of an investor who uses it is a submartingale regardless of the strategies of the other investors, and the relative wealth of any other essentially different strategy vanishes asymptotically. This strategy can be considered as an optimal growth portfolio in the model.

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  • Mikhail Zhitlukhin, 2020. "A continuous-time asset market game with short-lived assets," Papers 2008.13230, arXiv.org.
    • Handle: RePEc:arx:papers:2008.13230
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    References listed on IDEAS

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    1. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "From discrete to continuous time evolutionary finance models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 913-931, May.
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    6. 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.
    7. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
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    11. Yaroslav Drokin & Mikhail Zhitlukhin, 2019. "Relative growth optimal strategies in an asset market game," Papers 1908.01171, arXiv.org, revised Jul 2020.
    12. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "Market selection of constant proportions investment strategies in continuous time," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 248-266, March.
    13. 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.
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    Cited by:

    1. Mikhail Zhitlukhin, 2021. "Asymptotically optimal strategies in a diffusion approximation of a repeated betting game," Papers 2108.11998, arXiv.org.
    2. Mikhail Zhitlukhin, 2021. "Capital growth and survival strategies in a market with endogenous prices," Papers 2101.09777, arXiv.org.

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