Comptes Rendus
no. 6
Partial differential equations/Numerical analysis
A new method for solving Kolmogorov equations in mathematical finance

Presented by: Olivier Pironneau

Philippe G. LeFloch1; Jean-Marc Mercier2
1 Laboratoire Jacques-Louis-Lions & Centre national de la recherche scientifique, Université Pierre-et-Marie-Curie, 4, place Jussieu, 75252 Paris cedex 05, France
2 MPG Partners, 136, bd Haussmann, 75008 Paris, France
Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 680-686.

For multi-dimensional Fokker–Planck–Kolmogorov equations, we propose a numerical method which is based on a novel localization technique. We present extensive numerical experiments that demonstrate its practical interest for finance applications. In particular, this approach allows us to treat calibration and valuation problems, as well as various risk measure computations.

Nous proposons une nouvelle méthode numérique, utilisant une technique de localisation originale, pour résoudre des équations de Fokker–Planck–Kolmogorov multi-dimensionnelles. Nous présentons des tests numériques extensifs qui démontrent l'intérêt pratique de cette approche pour les applications en finance. En particulier, cette approche nous permet de traiter les problèmes de calibration et de valorisation, ainsi que le calcul de mesures de risque variées.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.05.003

Philippe G. LeFloch 1; Jean-Marc Mercier 2

1 Laboratoire Jacques-Louis-Lions & Centre national de la recherche scientifique, Université Pierre-et-Marie-Curie, 4, place Jussieu, 75252 Paris cedex 05, France
2 MPG Partners, 136, bd Haussmann, 75008 Paris, France 
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Philippe G. LeFloch; Jean-Marc Mercier. A new method for solving Kolmogorov equations in mathematical finance. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 680-686. doi : 10.1016/j.crma.2017.05.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.05.003/

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