A new formulation of asset trading games in continuous time with essential forcing of variation exponent
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.
|Date of creation:||Aug 2007|
|Date of revision:||Jan 2010|
|Publication status:||Published in Bernoulli 2009, Vol. 15, No. 4, 1243-1258|
|Contact details of provider:|| Web page: http://arxiv.org/|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29.
- 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.
- Yasunori Horikoshi & Akimichi Takemura, 2007. "Implications of contrarian and one-sided strategies for the fair-coin game," Papers math/0703743, arXiv.org.
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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.