Stochastic tools for financial economics

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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.