Stochastic and Mathematical Structures from and for Financial Economics

我的研究提案包括四个在意义上具有同等价值的项目。对于这些项目，我的主要目标是构建新的随机概念/概念/工具，并开发由经济和金融现象/假设/行为诱导的随机/数学结构。 第一个主题讨论了最优投资组合和/或最优消费中的水平依赖关系。自上世纪30年代以来，人们就知道，由于许多人类和社会原因，地平线的长短对投资和消费有巨大影响。欧文·费舍尔在他的《一般风险收益》一书中写道：“期待短暂生存的水手或士兵将不太可能进行永久性投资……只有低价格，即高利率，才会诱使他进行长期投资。”在这个项目中，我建议继续我在这个问题上的工作，以便尽可能明确地挑出地平线的长度如何影响最优投资组合选择和最优消费。这将使我们能够更好地应对/面对其他与前景相关的风险，如违约、死亡和信用风险。 我的第二个项目关注的是信息市场及其监管。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收费来监管信息不对称。在这个项目中，我建议研究当交易成本有效时，信息与市场效率之间的相互作用。这将增进我们对这些市场的了解，以便设计适当的交易成本/税收制度，恢复信息不对称市场的效率。这些预测结果将得到可靠的随机和数学论证的支持，并将在政治经济学、公共经济学和决策领域加强关于信息市场的现有经济学观点。 第三个主要项目涉及习惯形成实用工具，在这里我将重点了解社会行为(如习惯、上瘾、贪婪、恐惧等)对消费者的影响。我计划开发创新的随机工具，量化这些社会/人类行为的影响。 第四个项目与行为金融学/经济学有关。建立在冯·诺伊曼和摩根斯坦公理基础上的期望效用理论未能解释人类的情感/心理以及许多悖论和谜题(如阿莱悖论、埃莱斯伯格悖论和股权溢价之谜)。因此，许多经济学家提出了替代欧盟技术的方案，这些方案得到了实证研究的支持，包括前景理论、安全潜力/期望理论和双重选择理论。由于效用函数缺乏全局凹性(例如，效用函数在某些情况下呈S形状)，所有为EUT设计的数学方法都在这些行为框架下失败。我在这个主题中预计的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。

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.