کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1156842 | 958880 | 2011 | 29 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Sequential optimizing strategy in multi-dimensional bounded forecasting games Sequential optimizing strategy in multi-dimensional bounded forecasting games](/preview/png/1156842.png)
We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001) [10]. By studying the asymptotic behavior of its capital process, we prove a generalization of the strong law of large numbers, where the convergence rate of the sample mean vector depends on the growth rate of the quadratic variation process. The growth rate of the quadratic variation process may be slower than the number of rounds or may even be zero. We also introduce an information criterion for selecting efficient betting items. These results are then applied to multiple asset trading strategies in discrete-time and continuous-time games. In the case of a continuous-time game we present a measure of the jaggedness of a vector-valued continuous process. Our results are examined by several numerical examples.
Journal: Stochastic Processes and their Applications - Volume 121, Issue 1, January 2011, Pages 155–183