英文标题：
《Financial market models in discrete time beyond the concave case》
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作者：
Mario Sikic
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最新提交年份：
2015
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英文摘要：
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables describing the outcome of trading. We do not make any concavity assumptions. The first result is that under sequential upper-semicontinuity the market model can be represented as a normal integrand. We then extend the concept of no-arbitrage to this setup and study its consequences as the super-hedging theorem and utility maximization. Finally, we show how to extend the concepts and results to the case of vector-valued market models, an example of which is the Kabanov model of currency markets.
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中文摘要：
在本文中，我们建议从一组公理开始研究市场模型，就像在风险度量的情况下一样。我们将市场模型简单地定义为从一组适应策略到一组描述交易结果的随机变量的映射。我们不做任何凹度假设。第一个结果是，在序列上半连续下，市场模型可以表示为正规被积函数。然后，我们将无套利的概念推广到这种情况，并研究其作为超级套期保值定理和效用最大化的后果。最后，我们展示了如何将这些概念和结果推广到向量值市场模型，货币市场的卡巴诺夫模型就是一个例子。
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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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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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