SANAF: Stochastic Analysis and Numerical Approximations in Mathematical Finance*

Start Date: 2011 End Date: 2014
PIs: Cláudia Philippart (IST/UTL), Dmitrry Kramkov (CMU)
Team: Instituto Superior Técnico of the Universidade Técnica de Lisboa (IST/UTL), Carnegie Mellon University (CMU)

Abstract:
The purpose of this project is to contribute and provide new developments of Mathematical Finance, in terms of theoretical results, computational applications and models, with special emphasis in Real Options. More precisely, we plan to address questions concerning the three following topics: 

    (i) Efficient numerical algorithms; 
    (ii) Investment decisions under uncertainty; 
    (iii) Interest rate models.

These are hot topics of research, especially in the present context, where the recent economical and finance world crisis raised new challenges. These challenges are of different types, and concern not only the need of new mathematical approaches (that account for different levels of uncertainty present in the markets, in order to assess the actual risk of bankruptcy of finance institutions), as well as computational applications (in order to help taking decisions in real-time).

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*Project approved in the Call 2009 in Applications of Mathematics Thematic Areas, in the framework of the Carnegie Mellon Portugal Program and UT Austin-Portugal