arXiv：cs.LG· Masahiro Kato·· 3 小时前AI 评分28
期望效用遗憾规则：Minimax 与 Bayes 最优投资组合选择
Expected Utility Regret Rule: Minimax and Bayes Optimal Portfolio Choice
AI 导读
研究提出期望效用遗憾（EUR）规则，可同时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 规则无需先验分布即可同时达到 minimax 与 Bayes 下界（含首项常数）。均值-方差与风险平价组合被推导为该框架的特例，当收益除以波动率的联合分布与资产顺序无关时，EUR 规则与风险平价组合一致。
正文
Abstract: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.
| Subjects: | Econometrics (econ.EM); Machine Learning (cs.LG); Statistics Theory (math.ST); Mathematical Finance (q-fin.MF); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.02290 [econ.EM] |
| (or arXiv:2610.02290v1 [econ.EM] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02290 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Masahiro Kato [view email]
[v1]
Thu, 1 Oct 2026 16:15:37 UTC (205 KB)
来源：arXiv：cs.LG · arxiv.org