Can I read Signature SDEs from an affine and polynomial perspective on EtoBox?

Signature SDEs from an affine and polynomial perspective by Cuchiero, Christa; Svaluto-Ferro, Sara; Teichmann, Josef is a scholarly article available to read on EtoBox.

What is Signature SDEs from an affine and polynomial perspective about?

Signature stochastic differential equations (SDEs) constitute a large class of stochastic processes, here driven by Brownian motions, whose characteristics are linear maps of their own signature, i.e. of iterated integrals of the process with itself, and allow therefore for a generic path dependence. We show that their prolongation with the corresponding signature is an affine and polynomial process taking values in the set of group-like elements of the extended tensor algebra. By relying on the duality theory for affine or polynomial processes, we obtain explicit formulas in terms of converging power series for the Fourier-Laplace transform and the expected value of entire functions of the signature process' marginals. The coefficients of these power series are solutions of extended tensor algebra valued Riccati and linear ordinary differential equations (ODEs), respectively, whose vector fields can be expressed in terms of the characteristics of the corresponding SDEs. We thus construct a class of stochastic processes which is universal (in a sense specified in the introduction) within Ito-diffusions with path-dependent characteristics and allows for an explicit characterization

Author

Cuchiero, Christa; Svaluto-Ferro, Sara; Teichmann, Josef

Published

2023

Language

EN