发表机构
The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出期望效用遗憾（EUR）规则，联合选择投资组合类别并估计权重，在正则参数模型中同时达到极小极大和贝叶斯下界，并涵盖均值-方差与风险平价投资组合作为特例。
AI 中文摘要
本研究考虑投资组合选择问题，即向投资者推荐一个投资组合以最大化其财富的期望效用。我们的目标是构建一个在期望效用遗憾（即预言式投资者的期望效用与根据数据选择的投资组合所实现的期望效用之间的差异）方面渐近最优的投资组合选择规则。我们提出了期望效用遗憾（EUR）规则，该规则联合选择投资组合类别并估计其权重。在正则参数化收益模型中，单一EUR规则同时达到极小极大和贝叶斯下界（包括其领先常数），而无需使用定义贝叶斯准则的先验分布。然后，我们将均值-方差和风险平价投资组合推导为该框架的特例。在平滑递增且凹的效用函数下，当期望超额收益足够快地趋近于零时，EUR规则与样本均值-方差投资组合达到相同的领先期望遗憾。当收益除以波动率后的联合分布不依赖于资产顺序时，EUR规则与风险平价投资组合一致。
英文摘要
This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean--variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean--variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide.
