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Maturity randomization for stochastic control problems

Bouchard, Bruno; Karoui, Nicole El; Touzi, Nizar (2005), Maturity randomization for stochastic control problems, The Annals of Applied Probability, 15, 4, p. 2575-2605. http://dx.doi.org/10.1214/105051605000000593

Type
Article accepté pour publication ou publié
Date
2005
Journal name
The Annals of Applied Probability
Volume
15
Number
4
Publisher
Institute of Mathematical Statistics
Pages
2575-2605
Publication identifier
http://dx.doi.org/10.1214/105051605000000593
Metadata
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Author(s)
Bouchard, Bruno
Karoui, Nicole El
Touzi, Nizar
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.
Subjects / Keywords
optimal stopping; uncertain volatility models; stochastic control

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