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Approximation by quantization of the filter process and applications to optimal stopping problems under partial observation

Author

Listed:
  • Pham Huyên

    (1. Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris 7 pham@math.jussieu.fr and CREST)

  • Runggaldier Wolfgang

    (2. Dipartimenta di Matematica Pura ed Applicata, Universita degli studi di Padova. runggal@math.unipd.it)

  • Sellami Afef

    (3. Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris 7. sellami@math.jussieu.fr)

Abstract

We present an approximation method for discrete time nonlinear filtering in view of solving dynamic optimization problems under partial information. The method is based on quantization of the Markov pair process filter-observation (Π, Y) and is such that, at each time step k and for a given size Nk of the quantization grid in period k, this grid is chosen to minimize a suitable quantization error. The algorithm is based on a stochastic gradient descent combined with Monte Carlo simulations of (Π, Y). Convergence results are given and applications to optimal stopping under partial observation are discussed. Numerical results are presented for a particular stopping problem: American option pricing with unobservable volatility.

Suggested Citation

  • Pham Huyên & Runggaldier Wolfgang & Sellami Afef, 2005. "Approximation by quantization of the filter process and applications to optimal stopping problems under partial observation," Monte Carlo Methods and Applications, De Gruyter, vol. 11(1), pages 57-81, March.
    • Handle: RePEc:bpj:mcmeap:v:11:y:2005:i:1:p:57-81:n:5
    DOI: 10.1515/1569396054027283
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    Citations

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    Cited by:

    1. Brandejsky, Adrien & de Saporta, Benoîte & Dufour, François, 2013. "Optimal stopping for partially observed piecewise-deterministic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3201-3238.
    2. Giorgia Callegaro & Abass Sagna, 2009. "An application to credit risk of a hybrid Monte Carlo-Optimal quantization method," Papers 0907.0645, arXiv.org.
    3. repec:hal:wpaper:hal-00400666 is not listed on IDEAS
    4. Ludkovski, Michael, 2009. "A simulation approach to optimal stopping under partial information," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4061-4087, December.

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