英文标题：
《Polynomial processes in stochastic portfolio theory》
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作者：
Christa Cuchiero
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最新提交年份：
2017
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英文摘要：
We introduce polynomial processes in the sense of [8] in the context of stochastic portfolio theory to model simultaneously companies\' market capitalizations and the corresponding market weights. These models substantially extend volatility stabilized market models considered by Robert Fernholz and Ioannis Karatzas in [18], in particular they allow for correlation between the individual stocks. At the same time they remain remarkably tractable which makes them applicable in practice, especially for estimation and calibration to high dimensional equity index data. In the diffusion case we characterize the joint polynomial property of the market capitalizations and the corresponding weights, exploiting the fact that the transformation between absolute and relative quantities perfectly fits the structural properties of polynomial processes. Explicit parameter conditions assuring the existence of a local martingale deflator and relative arbitrages with respect to the market portfolio are given and the connection to non-attainment of the boundary of the unit simplex is discussed. We also consider extensions to models with jumps and the computation of optimal relative arbitrage strategies.
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中文摘要：
我们在随机投资组合理论的背景下引入了[8]意义上的多项式过程，以同时模拟公司的市场资本化和相应的市场权重。这些模型在很大程度上扩展了Robert Fernholz和Ioannis Karatzas在[18]中考虑的波动稳定市场模型，特别是它们考虑了各个股票之间的相关性。同时，它们仍然具有显著的可处理性，这使得它们在实践中适用，尤其是对高维股票指数数据的估计和校准。在扩散情况下，我们利用绝对量和相对量之间的转换完全符合多项式过程的结构性质这一事实，刻画了市场资本化和相应权重的联合多项式性质。给出了关于市场投资组合存在局部鞅平减指数和相对套利的显式参数条件，并讨论了与单位单纯形边界未达到的关系。我们还考虑了带跳跃模型的扩展和最优相对套利策略的计算。
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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：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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