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Stochastic securities market model with no short-selling.

机译：没有卖空的随机证券市场模型。

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摘要

The connection between martingale theory and the notion of arbitrage has been an area of extensive research ever since the seminal works by Kreps (1981) and Harrison and Pliska (1981). In particular, we look at the Fundamental Theorem of Asset Pricing, which states that a market has no arbitrage if and only if there is an equivalent probability measure under which the price process is a martingale. Jouini and Kallal (1995), as well as Carassus, Pham, and Touzi (2001) have studied this theorem in the presence of trading constraints. Specifically, they show that if investors are not allowed to short sell assets then the market satisfies no feasible arbitrage if and only if there is an equivalent probability measure under which the price process is a supermartingale.;This dissertation provides a new, versatile framework that strengthens and expands this theorem. Not only does it provide a simpler proof of the result, but it also demonstrates conditions under which the supermartingale property can be strengthened into a martingale property. This work also highlights certain applications of this theorem. In particular, it applies the theorem to the study of bid-ask spreads and pricing bubbles. It then extends the result to an infinite time horizon, using state price deflators. It finally concludes with a discussion of how to price assets, using state price deflators and linear programming techniques.;Keywords: Fundamental Theorem of Asset Pricing, martingale, arbitrage, short selling, state price deflator.
机译：自从Kreps（1981）和Harrison and Pliska（1981）开创性的著作以来，mar理论和套利概念之间的联系一直是广泛研究的领域。特别是，我们看一下资产定价的基本定理，该定理指出，当且仅当存在等同的概率测度（在该测度下价格过程是a），市场才没有套利。 Jouini和Kallal（1995）以及Carassus，Pham和Touzi（2001）在存在交易约束的情况下研究了该定理。具体而言，他们表明，如果不允许投资者做空资产，那么，并且仅当存在一种等效的概率度量，即价格过程是超级市场时，市场才能满足不可行的套利。加强和扩展了该定理。它不仅提供了更简单的结果证明，而且还展示了将超级property头财产增强为a头财产的条件。这项工作还强调了该定理的某些应用。特别是，它将定理应用于买卖差价和价格泡沫的研究。然后，使用州价格平减器将结果扩展到无限的时间范围。最后，最后讨论了如何使用状态价格平减器和线性规划技术对资产进行定价。关键词：资产定价基本定理，ting，套利，卖空，状态价格平减指数。

著录项

  • 作者

    Mcclintock, Scott Daniel.;

  • 作者单位

    University of Kentucky.;

  • 授予单位 University of Kentucky.;
  • 学科 Statistics.;Finance.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 70 p.
  • 总页数 70
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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