IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0708.0275.html
   My bibliography  Save this paper

A new formulation of asset trading games in continuous time with essential forcing of variation exponent

Author

Listed:
  • Kei Takeuchi
  • Masayuki Kumon
  • Akimichi Takemura

Abstract

We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can depend on the past path of the market. We prove that an investor can essentially force that the asset price path behaves with the variation exponent exactly equal to two. Our proof is based on embedding high-frequency discrete-time games into the continuous-time game and the use of the Bayesian strategy of Kumon, Takemura and Takeuchi (Stoch. Anal. Appl. 26 (2008) 1161--1180) for discrete-time coin-tossing games. We also show that the main growth part of the investor's capital processes is clearly described by the information quantities, which are derived from the Kullback--Leibler information with respect to the empirical fluctuation of the asset price.

Suggested Citation

  • Kei Takeuchi & Masayuki Kumon & Akimichi Takemura, 2007. "A new formulation of asset trading games in continuous time with essential forcing of variation exponent," Papers 0708.0275, arXiv.org, revised Jan 2010.
    • Handle: RePEc:arx:papers:0708.0275
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0708.0275
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. V. Vovk, 1993. "Forecasting point and continuous processes: Prequential analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 189-217, December.
    2. Yasunori Horikoshi & Akimichi Takemura, 2007. "Implications of contrarian and one-sided strategies for the fair-coin game," Papers math/0703743, arXiv.org.
    3. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    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. Vladimir Vovk, 2007. "Continuous-time trading and emergence of randomness," Papers 0712.1275, arXiv.org, revised Dec 2007.
    2. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.

    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. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
    2. Jin’an He & Shicheng Yin & Fangping Peng, 2024. "Weak aggregating specialist algorithm for online portfolio selection," Computational Economics, Springer;Society for Computational Economics, vol. 63(6), pages 2405-2434, June.
    3. Seung-Hyun Moon & Yong-Hyuk Kim & Byung-Ro Moon, 2019. "Empirical investigation of state-of-the-art mean reversion strategies for equity markets," Papers 1909.04327, arXiv.org.
    4. Man Yiu Tsang & Tony Sit & Hoi Ying Wong, 2022. "Adaptive Robust Online Portfolio Selection," Papers 2206.01064, arXiv.org.
    5. Luo, Yong & Zhu, Bo & Tang, Yong, 2014. "Simulated annealing algorithm for optimal capital growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 10-18.
    6. Fabio Stella & Alfonso Ventura, 2011. "Defensive online portfolio selection," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 2(1/2), pages 88-105.
    7. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2024. "Quantifying dimensional change in stochastic portfolio theory," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 977-1021, July.
    8. Ormos, Mihály & Urbán, András & Zoltán, Tamás, 2009. "Logoptimális portfóliók empirikus vizsgálata [Empirical analysis of log-optimal portfolios]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 1-18.
    9. Fereydooni, Ali & Barak, Sasan & Asaad Sajadi, Seyed Mehrzad, 2024. "A novel online portfolio selection approach based on pattern matching and ESG factors," Omega, Elsevier, vol. 123(C).
    10. Jarrod Wilcox, 2020. "Better portfolios with higher moments," Journal of Asset Management, Palgrave Macmillan, vol. 21(7), pages 569-580, December.
    11. Dmitry B. Rokhlin, 2021. "Relative utility bounds for empirically optimal portfolios," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 437-462, June.
    12. Vladimir V'yugin, 2014. "Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem," Papers 1410.5996, arXiv.org, revised Jun 2015.
    13. R'emi J'ez'equel & Dmitrii M. Ostrovskii & Pierre Gaillard, 2022. "Efficient and Near-Optimal Online Portfolio Selection," Papers 2209.13932, arXiv.org.
    14. Miquel Noguer i Alonso & Sonam Srivastava, 2020. "Deep Reinforcement Learning for Asset Allocation in US Equities," Papers 2010.04404, arXiv.org.
    15. Malo Huard & Rémy Garnier & Gilles Stoltz, 2020. "Hierarchical robust aggregation of sales forecasts at aggregated levels in e-commerce, based on exponential smoothing and Holt's linear trend method," Working Papers hal-02794320, HAL.
    16. Christopher Dance & Alexei Gaivoronski, 2012. "Stochastic optimization for real time service capacity allocation under random service demand," Annals of Operations Research, Springer, vol. 193(1), pages 221-253, March.
    17. James Chok & Geoffrey M. Vasil, 2023. "Convex optimization over a probability simplex," Papers 2305.09046, arXiv.org.
    18. Shmilovici Armin & Ben-Gal Irad, 2012. "Predicting Stock Returns Using a Variable Order Markov Tree Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(5), pages 1-33, December.
    19. Bin Li & Steven C. H. Hoi, 2012. "On-Line Portfolio Selection with Moving Average Reversion," Papers 1206.4626, arXiv.org.
    20. Alex Garivaltis, 2018. "Super-Replication of the Best Pairs Trade in Hindsight," Papers 1810.02444, arXiv.org, revised Oct 2022.

    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:0708.0275. 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.