Design of new models and techniques for high performance financial applications.

In the past decennia the international financial markets are witnessing a huge increase in the trading of more and more complex products, such as exotic options and interest products, and this growth is only amplifying. For the exchanges and banks it is of crucial importance to be able to price these products accurately, and as fast as possible. The simulation of the current, sophisticated pricing models is, however, very time consuming with classical techniques such as Monte Carlo methods or binomial trees, and practical pricing formulas are often not at hand. This project is concerned with new models and techniques for robustly and efficiently pricing modern financial products. We investigate two complementary approaches: the first is based on partial differential equations and the second on quantum mechanical path integrals. In the first approach, we will consider operator splitting methods and meshfree methods for the effective numerical solution of these, often multi-dimensional, equations. In the second approach, path integral formulas for financial products will be studied by using the present theory concerning physical multi-particle systems and the comonotonicity coefficient. The obtained models and computational techniques will continually be mutually validated.

Keywords:NUMERICAL ANALYSIS

Disciplines:Applied mathematics in specific fields, Computer architecture and networks, Distributed computing, Information sciences, Information systems, Programming languages, Scientific computing, Theoretical computer science, Visual computing, Other information and computing sciences