Section: New Results

Rational Approximation for fitting Non Negative EPT densities

Participants : Martine Olivi, Bernard Hanzon [Univ. Cork] , Conor Sexton [Univ. Cork] , Fabien Seyfert.

We explored this year a new application field for our rational approximation methods. We studied the problem of fitting a probability density function from a large set of financial data. The class of density function that we considered is that of non negative EPT (Exponential-Trigonometric-Polynomials) functions that seems to provide a very relevant framework for probabilistic calculations. Parseval's theorem implies that approximating the rational transform is equivalent to approximating the density itself. During his visit, Conor Sexton (a PHD student of Bernard Hanzon) adapted and ran the RARL2 software on this problem. The results were encouraging albeit the major problem of imposing positivity is still under study.