Stochastic and Mathematical Structures from and for Financial Economics

点击翻译按钮获取中文摘要

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.