Wednesday, April 27th 2005.

Speaker : Przemek Repetowicz
(Research Associate, Department of Physics, The University of Dublin, Trinity College)

Title : Diagrammatic perturbative expansions of phi^4 field theories versus multivariate stochastic inference of covariances in not-Gaussian and/or stable Paretian time series.

Abstract : Statistical properties of a system of coupled an-harmonic oscillators coupled to a thermal bath were well described by means of expansions of the partition function into Feynman diagrams [1]. A careful enumeration of graphs, a removal of divergencies occuring in the integral weights, by means of a computer program, has lead to efficient methods of assessing critical exponents of the field theories in different dimensions. This is well known for decades as the phi^4 theory in 4-epsilon dimensions.

Recently, it has been recognised, that the problem of assessing covariances of a not-Gaussian multivariate distribution whose logarithmic characteristic function is a polynomial of order 2p is equivalent to computing the partition function of a phi^(2p) theory in the Fourier space. This allows for deriving new assessment procedures in multivariate stochastic analysis and for appling the results to the problem of optimising portfolios a la Markowitz (maximise the return of a portfolio subject to a given variance of it) and to duration immunisation (optimise an annuity that is required in return for a given life assurance instrument). The predictibility of the methods overcomes the that of standard econometrics' AutoRegressive Conditional Heteroskedastic (ARCH) extrapolation procedures.

[1] Kleinert H, Critical Properties of Phi^4 Theories, World Scientific, Singapore, 2001

Location and time : Wednesday, April 27th, at 15:00 in L2.41

Mail nmcmahon@computing.dcu.ie for more information.