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Probability and Computational Finance Seminar
Sergio Pulido Swiss Finance Institute @ EPFL Title: Polynomial preserving processes on quadric sets Abstract: Polynomial preserving processes are time-homogeneous Markov jump-diffusions whose generator leaves the space of polynomials of any fixed degree invariant. The polynomial preserving property leads to tractability in a financial modeling context. Affine processes are particular examples of polynomial preserving processes. In contrast to affine models, however, there exist examples of polynomial preserving models on a larger class of state spaces, for example compact sets. In this work, we characterize the polynomial preserving diffusions whose state space is a quadric set, e.g. the unit ball. The interplay of algebraic and geometric considerations plays an essential role in our analysis. In particular, we find strong connections to the classical problem of expressing nonnegative polynomials as sums of squares, which highlights the interest of our results from an algebraic point of view. This is joint work with Martin Larsson. Date: Monday, November 10, 2014 Time: 5:00 pm Location: Porter Hall 226C Submitted by: Dmitry Kramkov |