• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

Time discretization and quantization methods for optimal multiple switching problem

Pham, Huyen; Kharroubi, Idris; Gassiat, Paul (2012), Time discretization and quantization methods for optimal multiple switching problem, Stochastic Processes and their Applications, 122, 5, p. 2019–2052. http://dx.doi.org/10.1016/j.spa.2012.02.008

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00626258/fr/
Date
2012
Journal name
Stochastic Processes and their Applications
Volume
122
Number
5
Publisher
Elsevier
Pages
2019–2052
Publication identifier
http://dx.doi.org/10.1016/j.spa.2012.02.008
Metadata
Show full item record
Author(s)
Pham, Huyen
Kharroubi, Idris
Gassiat, Paul
Abstract (EN)
In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time approximation of the optimal switching problem, and analyze its rate of convergence. The error is of order $\frac{1}{2} - \eps$, $\eps$ $>$ $0$, and of order $1\over 2$ when the switching costs do not depend on the state process. We next propose quantization numerical schemes for the space discretization of the discrete-time Euler state process. A Markovian quantization approach relying on the optimal quantization of the normal distribution arising in the Euler scheme is analyzed. In the particular case of uncontrolled state process, we describe an alternative marginal quantization method, which extends the recursive algorithm for optimal stopping problems as in Bally-Pagès (2004). A priori $L^p$-error estimates are stated in terms of quantization errors. Finally, some numerical tests are performed for an optimal switching problem with two regimes.
Subjects / Keywords
numerical probability; Markov chains; discrete-time approximation; quantization of random variables; Optimal switching

Related items

Showing items related by title and author.

  • Thumbnail
    A probabilistic numerical method for optimal multiple switching problem in high dimension 
    Aïd, René; Campi, Luciano; Langrené, Nicolas; Pham, Huyên (2014) Article accepté pour publication ou publié
  • Thumbnail
    Optimal investment under multiple defaults risk: a BSDE-decomposition approach 
    Jiao, Ying; Kharroubi, Idris; Pham, Huyen (2013) Article accepté pour publication ou publié
  • Thumbnail
    BSDE representations for optimal switching problems with controlled volatility 
    Kharroubi, Idris; Elie, Romuald (2014) Article accepté pour publication ou publié
  • Thumbnail
    Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps 
    Kharroubi, Idris; Langrené, Nicolas; Pham, Huyên (2015) Article accepté pour publication ou publié
  • Thumbnail
    Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE 
    Kharroubi, Idris; Pham, Huyen (2015) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo