摘要翻译:
在$L_\infty$-框架中,我们给出了线性算子的几个推广定理。我们把注意力集中在保多数和保三明治类型的扩张上。然后将这些结果应用于价格系统的研究,得到了合理限制等价鞅测度的一类适用。首先,我们考虑了密度有界的等价鞅测度及其相应的价格以线性极大值和极大值为界的等价鞅测度。然后我们考虑了受买卖动力学约束的价格。最后,在夏普比给定的范围内,我们研究了与非好交易定价措施相一致的价格系统。在本研究中,我们引入了动态不良交易定价测度的定义。
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英文标题:
《Extension theorems for linear operators on $L_\infty$ and application to
price systems》
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作者:
Jocelyne Bion-Nadal and Giulia Di Nunno
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最新提交年份:
2011
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分类信息:
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: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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英文摘要:
In an $L_\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures applicable. First we consider equivalent martingale measures with bounds on densities and the corresponding prices bounded by linear minorant and majorant. Then we consider prices bounded by bid-ask dynamics. Finally we study price systems consistent with no-good-deal pricing measures for given bounds on the Sharpe ratio. Within this study we introduce the definition of dynamic no-good-deal pricing measure.
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PDF链接:
https://arxiv.org/pdf/1102.5501