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Maturity randomization for stochastic control problems

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Date
2005
Dewey
Probabilités et mathématiques appliquées
Sujet
optimal stopping; uncertain volatility models; stochastic control
Journal issue
The Annals of Applied Probability
Volume
15
Number
4
Publication date
2005
Article pages
2575-2605
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/105051605000000593
URI
https://basepub.dauphine.fr/handle/123456789/3460
Collections
  • CEREMADE : Publications
Metadata
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Author
Bouchard, Bruno
Karoui, Nicole El
Touzi, Nizar
Type
Article accepté pour publication ou publié
Abstract (EN)
We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called {\it Canadization} procedure suggested by P. Carr in [2] for the fast computation of American put option prices. In addition to the original application of this technique to optimal stopping problems, we provide an application to another problem in finance, namely the super-replication problem under stochastic volatility, and we show that the approximating value functions can be computed explicitly.

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