论文标题
经验最佳投资组合的相对效用界限
Relative utility bounds for empirically optimal portfolios
论文作者
论文摘要
我们考虑投资者的单期投资组合选择问题，最大程度地提高了投资组合实用程序的预期比率以及事后获得最佳资产的实用性。决策规则基于股票回报的历史，分配未知。假设效用函数是Lipschitz或Hölder连续的（不需要凹度），我们在唯一假设上获得了回报是独立且分布相同的唯一假设下获得的高概率效用界限。这些界限仅取决于效用函数，资产数量和观察次数。对于凹面实用程序，对于通过指示梯度方法产生的投资组合获得了相似的边界。另外，我们使用统计实验来研究经验上最佳投资组合的风险和概括特性。在此，我们考虑一个具有一个风险资产和一个数据集的模型，其中包含来自纽约证券交易所的股票价格。
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns with unknown distribution. Assuming that the utility function is Lipschitz or Hölder continuous (the concavity is not required), we obtain high probability utility bounds under the sole assumption that the returns are independent and identically distributed. These bounds depend only on the utility function, the number of assets and the number of observations. For concave utilities similar bounds are obtained for the portfolios produced by the exponentiated gradient method. Also we use statistical experiments to study risk and generalization properties of empirically optimal portfolios. Herein we consider a model with one risky asset and a dataset, containing the stock prices from NYSE.
