摘要翻译：
在一篇开创性的论文中，Cover and Ordentlich（1998）解决了交易者（选择整个交易算法$theta(\CDOT)$)和“自然”之间的最大-最小投资组合博弈，“自然”选择所有时期所有股票的总回报矩阵$x$。他们的（零和）游戏的回报核心是$W_\theta(X)/D(X)$，其中$W_\theta(X)$是交易者的最终财富，而$D(X)$是最终财富，这些财富会累积到一美元，存入事后确定的最佳常数再平衡投资组合（或固定分数下注方案）中。由此产生的“万能投资组合”以与事后最佳再平衡规则相同的渐近速度复合其资金，从而在极其一般的条件下渐近地击败市场。受这一结果（1998）的影响，本文解决了复盖和Ordentlich(1998)最大-最小对策的最一般可处理版本。这是为了在每个时期的总回报向量中分别凸和齐次的性能基准（阅读：导数）而得到的。对于完全任意的（甚至不可测量的）业绩基准，我们展示了如何使用选择公理为交易者“找到”一个精确的最大化策略。
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英文标题：
《Multilinear Superhedging of Lookback Options》
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作者：
Alex Garivaltis
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最新提交年份：
2018
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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英文摘要：
  In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_\theta(X)/D(X)$, where $W_\theta(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit into the best constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. The resulting "universal portfolio" compounds its money at the same asymptotic rate as the best rebalancing rule in hindsight, thereby beating the market asymptotically under extremely general conditions. Smitten with this (1998) result, the present paper solves the most general tractable version of Cover and Ordentlich's (1998) max-min game. This obtains for performance benchmarks (read: derivatives) that are separately convex and homogeneous in each period's gross-return vector. For completely arbitrary (even non-measurable) performance benchmarks, we show how the axiom of choice can be used to "find" an exact maximin strategy for the trader.
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PDF链接：
https://arxiv.org/pdf/1810.02447