Stochastic and Mathematical Structures from and for Financial Economics

金融经济学中的随机和数学结构

• 批准号: RGPIN-2014-04987
• 负责人: Choulli, Tahir
• 金额: $ 0.8万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=588141
• 关键词: Stochastic; Mathematical; Structures; Financial; Economics

My research proposal consists of four projects with equal merit with regard to significance. For these projects, my main goal lies in building new stochastic notions/concepts/tools and developing the stochastic/mathematical structures induced by the economical and financial phenomena/assumptions/behaviors. The first topic addresses the horizon-dependence in optimal portfolio and/or optimal consumption. It was known, since the thirties of the last century, that the length of the horizon has a tremendous impact on investment and consumption due to many human and social reasons. In his book on general risk income, Irving Fisher wrote: "The sailor or the soldier who looks forward to a short existence will be less likely to make permanent investments.... Only a low price, that is, a high rate of interest, will induce him to invest for long ahead". In this project, I propose to continue my work on this issue in order to single out as explicitly as possible how the horizon's length affects the optimal portfolio choice and the optimal consumption. This will allow us to better address/face other horizon-related risks such as default, death and credit risk. My second project focuses on informational markets and their regulations. In real world, the US government forbids insider trading, while the economic literature suggests regulating the asymmetric information through taxes and fees. In this project, I propose to investigate the interplay between the information and the market's efficiency when the transaction costs are in-force. This will enhance our understanding of these markets in order to design adequate transaction costs/taxes regimes that will restore the efficiency in markets with asymmetric information. These projected results will be supported by solid stochastic and mathematical arguments, and will strengthen the existing economical ideas about the informational markets in the areas of political economy, public economy and decision making. The third main project deals with habit formation utilities, where I will focus on understanding the effect of the social behaviors (such as habit, addiction, greed, fear,..., etcetera) on the consumer. I am planning to develop innovative stochastic tools that will quantify the effect of these social/human behaviors. The fourth project is concerned with behavioral finance/economics. The Expected Utility Theory (EUT), which is based on the von Neumann and Morgenstern axioms, fails to explain human emotions/psychology and many paradoxes and puzzles (such as the Allais paradox, the Ellesberg paradox and the equity premium puzzle). Thus, many economists proposed alternatives to the EUT which (are supported by empirical studies and) include Prospect Theory, Security Potential/Aspiration Theory and Dual Theory of Choice. Due to the lack of global concavity in the utility function (which takes the S shape in some context for instance), all the mathematical approaches designed for the EUT fail in these behavioral frameworks. My projected contribution in this theme lies in producing new stochastic concepts and/or reliable mathematical methods for explaining these behavioral models and their impacts as well.

我的研究建议包括四个在重要性方面具有同等优点的项目。对于这些项目，我的主要目标在于建立新的随机概念/概念/工具，并开发由经济和财务现象/假设/行为引起的随机/数学结构。 第一个主题解决了最佳投资组合和/或最佳消费中的视野依赖性。自从上个世纪的三十世纪以来，人们知道地平线的长度对许多人类和社会原因对投资和消费产生了巨大影响。欧文·费舍尔（Irving Fisher）在有关一般风险收入的书中写道：“期待短暂存在的水手或士兵将不太可能进行永久投资。...只有低价，即高利率，才能促使他为早已投资。” 在这个项目中，我建议继续在此问题上进行工作，以便尽可能明确地挑出地平线长度如何影响最佳投资组合选择和最佳消费。这将使我们能够更好地解决/面对其他与视野有关的风险，例如违约，死亡和信用风险。 我的第二个项目着重于信息市场及其法规。 在现实世界中，美国政府禁止内幕交易，而经济文献则建议通过税收和费用来规范不对称信息。在这个项目中，我建议在交易成本无效时调查信息与市场效率之间的相互作用。这将增强我们对这些市场的理解，以设计适当的交易成本/税收制度，以通过不对称信息恢复市场效率。这些预计的结果将得到坚实的随机和数学论点的支持，并将加强有关政治经济学，公共经济和决策领域中信息市场的现有经济思想。 第三个主要项目涉及习惯形成公用事业，我将专注于了解社会行为的影响（例如习惯，成瘾，贪婪，恐惧，...等）。我计划开发创新的随机工具，以量化这些社会/人类行为的影响。 第四个项目与行为金融/经济学有关。基于冯·诺伊曼（Von Neumann）和摩根斯特（Morgenstern）公理的预期效用理论（EUT）未能解释人类的情绪/心理学以及许多悖论和难题（例如Allais Paradox，Ellesberg Paradox和Equity Premium Pubzle）。因此，许多经济学家提出了EUT的替代方案，该替代方案（得到经验研究的支持），包括前景理论，安全潜力/愿望理论和选择的双重理论。由于效用函数缺乏全局凹度（例如在某些情况下以S形状为例），因此在这些行为框架中为EUT设计的所有数学方法都失败了。我在这个主题中的预计贡献在于产生新的随机概念和/或可靠的数学方法来解释这些行为模型及其影响。