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摘要翻译：
本文提出了两种方法，在最小假设和一般连续时间市场模型下，定量地说明不存在套利和/或不存在投资组合的生存能力之间的确切关系。确切地说，我们的第一贡献和主要贡献证明了在一个等价的概率测度下，对于任何“好”效用和正的初始资本，非无界利润-有界风险条件（以下简称NUPBR）与NUM\'Eraire投资组合的存在性以及最优投资组合的存在性之间的等价性。在这里，一个“好”效用是满足Inada条件和Kramkov和Schachermayer弹性假设的任何光滑von Neumann-Morgenstern效用。此外，效用最大化问题在其下有解的等价概率测度可以根据我们的需要选择接近于现实世界的概率测度（但可能不相等）。在不改变潜在概率测度的情况下，在温和的假设下，我们的第二个贡献证明了NUPBR等价于最优投资组合的“{it局部}”存在性。如果一个人坚持在现实世界的概率下工作，这就构成了第一个贡献的替代方案。这两种贡献自然导致了新类型的生存能力，我们称之为弱生存能力和局部生存能力。
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英文标题：
《How Non-Arbitrage, Viability and Num\'eraire Portfolio are Related》
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作者：
Tahir Choulli, Jun Deng and Junfeng Ma
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最新提交年份：
2014
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分类信息：
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：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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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：
This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the num\'eraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence among the No-Unbounded-Profit-with-Bounded-Risk condition (NUPBR hereafter), the existence of the num\'eraire portfolio, and the existence of the optimal portfolio under an equivalent probability measure for any "nice" utility and positive initial capital. Herein, a 'nice" utility is any smooth von Neumann-Morgenstern utility satisfying Inada's conditions and the elasticity assumptions of Kramkov and Schachermayer. Furthermore, the equivalent probability measure ---under which the utility maximization problems have solutions--- can be chosen as close to the real-world probability measure as we want (but might not be equal). Without changing the underlying probability measure and under mild assumptions, our second contribution proves that the NUPBR is equivalent to the "{\it local}" existence of the optimal portfolio. This constitutes an alternative to the first contribution, if one insists on working under the real-world probability. These two contributions lead naturally to new types of viability that we call weak and local viabilities.
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PDF链接：
https://arxiv.org/pdf/1211.4598
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