Sequential optimizing strategy in multi-dimensional bounded forecasting games
Sequential optimizing strategy in multi-dimensional bounded forecasting games
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多维有界预测博弈中的序贯优化策略
DOI：
10.1016/j.spa.2010.09.004
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
A.
中科院分区：
文献类型：
--
作者：
Kumon;M.;Takemura;A.
我们在Shafer和Vovk（2001）[10]的博弈论概率框架中提出了多维有界预测博弈中的顺序优化投注策略。通过研究其资本过程的渐近性态，证明了强大数定律的一个推广，其中样本均值向量的收敛速度依赖于二次变分过程的增长速度。二次变异过程的增长率可能比轮数慢，甚至可能为零。我们还介绍了一个信息标准，选择有效的投注项目。然后将这些结果应用于离散时间和连续时间博弈中的多资产交易策略。在连续时间的游戏的情况下，我们提出了一个向量值连续过程的锯齿性的措施。我们的结果进行了检查的几个数值例子。
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.