Stochastic tools for financial economics

我的研究建议的主要和总体目标在于尽可能精确地量化金融经济模型中额外不确定性的影响。准确地说，我将专注于来自随机视野的额外信息/不确定性。投资者会受到不同类型的退出时间和风险的影响。在真实的生活中，退出时间的例子很多，例如死亡的时间，预期或意外的退休时间，投资者被解雇的时间，或者-一般来说-投资者被迫清算资产并退出市场的任何随机时间。每个退出时间都有其特定的风险，其影响是未知的，也不知道这个随机时间本身的建模。我们的目标是分析退出时间对最优消费的影响，并得出这些在公共经济和财政中的应用。我的方法是基于鞅理论，正是对家庭的鞅措施，我介绍和发展罢工者在一些文件。 为了实现这一经济目标，我将解决我的方法和拟议研究的步骤提出的数学挑战和问题。我将通过这项研究建立不同概念之间的联系（如随机地平线问题与不确定性模型）。随机视界问题有许多应用，例如在信用风险中，我将探索这些应用，并使用新的方法在这些领域做出贡献。

The main and general goal of my research proposal lies in quantifying, as precise as possible, the effect of additional uncertainty in a financial economic model. Precisely, I will focus on the additional information/uncertainty coming from the random horizons. An investor is subject to different kind of exit times and the risk they induce. In real life, exit time examples are numerous such as death's time, expected or unexpected retirement time, the time when the investor is fired from her job, or -general speaking- any random time when the investor is forced to liquidate her assets and quit the market. Each exit time has its specific risk, whose effect is not known nor the modeling of this random time itself. Our goal is to analyze the effect of exit time on the optimal consumption, and to draw the applications of these in Public Economic and Finance. My approach is based on the martingale theory, and precisely on the family of martingale measures that I introduced and developed with Striker in a number of papers. To achieve this economical goal, I will address the mathematical challenges and problems that are put forward by my methods and the steps of the proposed study. I will establish connection between different concepts through this study (such as random horizon problem vs uncertainty models). The problem of random horizons has many applications, such as in credit risk, and I will explore these applications and contribute in these areas using new method.