英文标题：
《Explicit description of all deflators for market models under random
  horizon with applications to NFLVR》
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作者：
Tahir Choulli and Sina Yansori
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最新提交年份：
2021
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英文摘要：
  This paper considers an initial market model, specified by its underlying assets $S$ and its flow of information $\\mathbb F$, and an arbitrary random time $\\tau$ which might not be an $\\mathbb F$-stopping time. As the death time and the default time (that $\\tau$ might represent) can be seen when they occur only, the progressive enlargement of $\\mathbb F$ with $\\tau$ sounds tailor-fit for modelling the new flow of information $\\mathbb G$ that incorporates both $\\mathbb F$ and $\\tau$. In this setting of informational market, the first principal goal resides in describing as explicitly as possible the set of all deflators for $(S^{\\tau}, \\mathbb G)$, while the second principal goal lies in addressing the No-Free-Lunch-with-Vanishing-Risk concept (NFLVR hereafter) for $(S^{\\tau}, \\mathbb G)$. Besides this direct application to NFLVR, the set of all deflators constitutes the dual set of all \"admissible\" wealth processes for the stopped model $(S^{\\tau},\\mathbb G)$, and hence it is vital in many hedging and pricing related optimization problems. Thanks to the results of Choulli et al. [7], on martingales classification and representation for progressive enlarged filtration, our two main goals are fully achieved in different versions, when the survival probability never vanishes. The results are illustrated on the two particular cases when $(S,\\mathbb F)$ follows the jump-diffusion model and the discrete-time model.
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中文摘要：
本文考虑了一个初始市场模型，该模型由其标的资产美元S$和信息流美元mathbb F$指定，以及一个任意的随机时间美元tau$，它可能不是美元mathbb F$停止时间。由于死亡时间和默认时间（即$\\tau$可能代表的时间）仅在发生时才可见，因此$\\mathb F$与$\\tau$的逐步扩大听起来非常适合建模新的信息流$\\mathbb G$，该信息流同时包含$\\mathb F$和$\\tau$。在这种信息市场环境中，第一个主要目标在于尽可能明确地描述美元的所有平减指数集，而第二个主要目标在于解决美元（S ^{\\tau}，\\mathbb G）$的无免费午餐和消失风险概念（NFLVR下文）问题。除了直接应用于NFLVR之外，所有平减指数集构成了停止模型$（S ^{\\tau}、\\mathbb G）$的所有“可容许”财富过程的对偶集，因此在许多对冲和定价相关的优化问题中至关重要。由于Choulli等人[7]关于逐步扩大过滤的鞅分类和表示的结果，我们的两个主要目标在不同版本中完全实现，此时生存概率永远不会消失。当$（S、\\mathbb F）$遵循跳跃扩散模型和离散时间模型时，结果在两种特殊情况下得到了说明。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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