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

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  • Mikhail Zhitlukhin

    (Steklov Mathematical Institute of the Russian Academy of Sciences)

Abstract

We propose a continuous-time game-theoretic model of an investment market with short-lived assets. The first goal of the paper is to obtain a stochastic equation which determines the 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.

Suggested Citation

  • Mikhail Zhitlukhin, 2022. "A continuous-time asset market game with short-lived assets," Finance and Stochastics, Springer, vol. 26(3), pages 587-630, July.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:3:d:10.1007_s00780-022-00479-6
    DOI: 10.1007/s00780-022-00479-6
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    References listed on IDEAS

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    1. Mikhail Zhitlukhin, 2021. "Survival Investment Strategies In A Continuous-Time Market Model With Competition," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(01), pages 1-24, February.
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    Cited by:

    1. Nina Badulina & Dmitry Shatilovich & Mikhail Zhitlukhin, 2024. "On convergence of forecasts in prediction markets," Papers 2402.16345, arXiv.org.
    2. I. V. Evstigneev & T. Hens & M. J. Vanaei, 2023. "Evolutionary finance: a model with endogenous asset payoffs," Journal of Bioeconomics, Springer, vol. 25(2), pages 117-143, August.

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    More about this item

    Keywords

    Asset market game; Relative growth optimal strategy; Martingale convergence; Evolutionary finance;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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