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Finance and Stochastics

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01.10.2012

Polynomial processes and their applications to mathematical finance

verfasst von: Christa Cuchiero, Martin Keller-Ressel, Josef Teichmann

Erschienen in: Finance and Stochastics | Ausgabe 4/2012

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Abstract

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 techniques for option pricing and hedging. For instance, the efficient and easy computation of moments can be used for variance reduction techniques in Monte Carlo methods.

Vorheriger Artikel Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles

Nächster Artikel The fundamental theorem of asset pricing under transaction costs

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All statements concerning the characteristics are meant up to an evanescent set.

We thank Martin Schweizer for pointing out this result to us.

We write here μ ₀ for the constant part of the jump measure in contrast to [7], where it is denoted by m.

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Titel: Polynomial processes and their applications to mathematical finance
verfasst von: Christa Cuchiero
Martin Keller-Ressel
Josef Teichmann
Publikationsdatum: 01.10.2012
Verlag: Springer-Verlag
Erschienen in: Finance and Stochastics / Ausgabe 4/2012
Print ISSN: 0949-2984
Elektronische ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-012-0188-x

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