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Bachelier Finance Society One World Seminar
Speaker: Christa Cuchiero

Title: Universality of affine and polynomial processes

We elaborate on universal properties of affine and polynomial processes. In several recent works we could show that many models which are at first sight not recognized as affine or polynomial can nevertheless be embedded in this framework. For instance, essentially all examples of (rough) stochastic volatility models can be viewed as (infinite dimensional) affine or polynomial processes. Moreover, all well-known measure-valued diffusions such as the Fleming–Viot process, the Super–Brownian motion, and the Dawson–Watanabe superprocess are affine or polynomial. This suggests an inherent universality of these model classes. We try to make this mathematically precise by showing that generic classes of diffusion models are projections of infinite dimensional affine processes (which in this setup coincide with polynomial processes). A key ingredient to establish this result is the signature process, well known from rough paths theory.

The talk is based on  joint works with Sara Svaluto-Ferro and Josef Teichmann.

Sep 10, 2020 07:00 PM in Zurich

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