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

Pham Huyên, Runggaldier Wolfgang and Sellami Afef
Additional contact information
Pham Huyên: 1. Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris 7 and CREST pham@math.jussieu.fr
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

Monte Carlo Methods and Applications, 2005, vol. 11, issue 1, 57-81

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.

Keywords: Nonlinear filtering; Markov chain; quantization; stochastic gradient descent; Monte Carlo simulations; partial observation; optimal stopping. (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://doi.org/10.1515/1569396054027283 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:11:y:2005:i:1:p:57-81:n:5

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/1569396054027283

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().