摘要翻译：
在金融市场的一般半鞅模型中，研究了可预测凸约束下的数字资产组合的存在性。数字投资组合产生一个财富过程，相对于该过程，所有其他投资组合的相对财富过程都是上鞅。利用资产价格过程的三重可预测特征，得到了数字资产组合存在的充要条件。然后，根据一个没有免费午餐的概念，这个特征被用来获得进一步的充要条件。特别是，不需要“没有风险消失的免费午餐”(NFLVR)的全部力量，只需要较弱的“没有风险有界的利润无界”(NUPBR)条件，该条件涉及财富过程的终值在概率上的有界性。我们证明了这个概念是进行效用优化所需的最小先验假设。事实上，它完全用可预测的特性来表示，这使得它很容易检查，这是更强的NFLVR条件所缺乏的。
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英文标题：
《The numeraire portfolio in semimartingale financial models》
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作者：
Ioannis Karatzas and Constantinos Kardaras
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最新提交年份：
2008
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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：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numeraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient conditions for the existence of the numeraire portfolio are obtained in terms of the triplet of predictable characteristics of the asset price process. This characterization is then used to obtain further necessary and sufficient conditions, in terms of a no-free-lunch-type notion. In particular, the full strength of the "No Free Lunch with Vanishing Risk" (NFLVR) is not needed, only the weaker "No Unbounded Profit with Bounded Risk" (NUPBR) condition that involves the boundedness in probability of the terminal values of wealth processes. We show that this notion is the minimal a-priori assumption required in order to proceed with utility optimization. The fact that it is expressed entirely in terms of predictable characteristics makes it easy to check, something that the stronger NFLVR condition lacks.
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PDF链接：
https://arxiv.org/pdf/0803.1877