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| HAL : hal-00288167, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Mesoscopic modelling of financial markets |
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| Stéphane Cordier 1Lorenzo Pareschi 2 |
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| Studium Collaboration(s) |
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| (15/06/2008) |
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| We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investments alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model under a suitable scaling we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis. |
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| 1 : | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| 2 : | Center for Modelling Computing and Statistics, c/o Department of Economy, Institutions and Territory |
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Università degli studi di Ferrara |
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| 3 : | Laboratoire d'économie d'Orleans (LEO) |
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CNRS : UMR6221 – Université d'Orléans |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Sciences de l'Homme et Société/Economies et finances |
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| wealth distribution – power-law tails – stock market – self-similarity – kinetic equations. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00288167, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00288167 | |
| oai:hal.archives-ouvertes.fr:hal-00288167 | |
| Contributeur : Stéphane Cordier | |
| Soumis le : Dimanche 15 Juin 2008, 22:46:59 | |
| Dernière modification le : Lundi 16 Juin 2008, 09:13:45 | |
