# Polynomial processes and their applications to mathematical finance

@article{Cuchiero2012PolynomialPA, title={Polynomial processes and their applications to mathematical finance}, author={Christa Cuchiero and Martin Keller-Ressel and Josef Teichmann}, journal={Finance and Stochastics}, year={2012}, volume={16}, pages={711-740} }

We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains affine processes, processes with quadratic diffusion coefficients, as well as Lévy-driven SDEs with affine vector fields. Thus, many popular models such as exponential Lévy models or affine models are covered by this setting. The applications range from statistical GMM estimation procedures to new…

## 115 Citations

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The martingale problem is known to be a classical and very powerful technology for the study of Markov processes through the analytical properties of the corresponding generators. This approach…

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