Markov cubature rules for polynomial processes

Damir Filipović (1, 2) , Martin Larsson (3) , Sergio Pulido (4, 5)

1 Swiss Financial Institute
2 EPFL - Ecole Polytechnique Fédérale de Lausanne
3 D-MATH - Department of Mathematics [ETH Zurich]
4 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
5 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment-matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study the existence of such rules using algebraic techniques. These rules aim to improve the tractability and ease the implementation of models where the underlying factors are polynomial processes.

Domaines: Probabilités [math.PR]

Damir Filipović, Martin Larsson, Sergio Pulido. Markov cubature rules for polynomial processes. 2016. ⟨hal-01418755v1⟩