Optimal Quantization Methods and Applications to Numerical Problems in Finance

  • Gilles Pagès
  • Huyên Pham
  • Jacques Printems


We review optimal quantization methods for numerically solving nonlinear problems in higher dimensions associated with Markov processes. Quantization of a Markov process consists in a spatial discretization on finite grids optimally fitted to the dynamics of the process. Two quantization methods are proposed: the first one, called marginal quantization, relies on an optimal approximation of the marginal distributions of the process, while the second one, called Markovian quantization, looks for an optimal approximation of transition probabilities of the Markov process at some points. Optimal grids and their associated weights can be computed by a stochastic gradient descent method based on Monte Carlo simulations. We illustrate this optimal quantization approach with four numerical applications arising in finance: European option pricing, optimal stopping problems and American option pricing, stochastic control problems and mean-variance hedging of options and filtering in stochastic volatility models.


Markov Chain Quantization Method Risky Asset Quantization Error Euler Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Gilles Pagès
    • 1
  • Huyên Pham
    • 1
  • Jacques Printems
    • 2
  1. 1.Laboratoire de Probabilités et Modèles Aléatoires CNRS, UMR 7599Université Paris 6Paris Cedex 05France
  2. 2.Centre de Mathématiques Faculté de Sciences et Technologie CNRS, UMR 8050Université Paris 12Créteil CedexFrance

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