论文标题
关于求解强大的对数最佳投资组合：支持超平面近似方法
On Solving Robust Log-Optimal Portfolio: A Supporting Hyperplane Approximation Approach
论文作者
论文摘要
{log-optimal}投资组合是最大化投资者财富预期对数增长（ELG）的任何投资组合。这个最大化问题通常假定交易者事先知道回报的真实分布信息。但是，实际上，返回分布确实是{模棱两可}；即，交易者未知的真实分布，或者最多部分地知道。为此，自然会出现{分布鲁棒的log-tim-optimal投资组合问题}。尽管问题表达考虑了回报分布的歧义，但问题通常不需要处理。为了解决这个问题，在本文中，我们提出了一种{支持的超平面近似}方法，该方法使我们能够将一类分布的强大日志式投资组合问题重新重新制定到线性程序中，该程序可以非常有效地解决。我们的框架足够灵活，可以允许{交易成本}，{杠杆和短路}，{roveral Trades}和{多元化注意事项}。另外，如果可接受的近似误差，则提供了一种有效的算法，用于快速计算最佳的超平面数量。还提供了一些使用历史股票价格数据的经验研究来支持我们的理论。
A {log-optimal} portfolio is any portfolio that maximizes the expected logarithmic growth (ELG) of an investor's wealth. This maximization problem typically assumes that the information of the true distribution of returns is known to the trader in advance. However, in practice, the return distributions are indeed {ambiguous}; i.e., the true distribution is unknown to the trader or it is partially known at best. To this end, a {distributional robust log-optimal portfolio problem} formulation arises naturally. While the problem formulation takes into account the ambiguity on return distributions, the problem needs not to be tractable in general. To address this, in this paper, we propose a {supporting hyperplane approximation} approach that allows us to reformulate a class of distributional robust log-optimal portfolio problems into a linear program, which can be solved very efficiently. Our framework is flexible enough to allow {transaction costs}, {leverage and shorting}, {survival trades}, and {diversification considerations}. In addition, given an acceptable approximation error, an efficient algorithm for rapidly calculating the optimal number of hyperplanes is provided. Some empirical studies using historical stock price data are also provided to support our theory.
