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Maturity randomization for stochastic control problems

By Bruno Bouchard, Nicole El Karoui and Nizar Touzi

Abstract

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

Topics: optimal stopping, stochastic control, uncertain volatility models, 93E20 35C15 91B28, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Publisher: HAL CCSD
Year: 2004
OAI identifier: oai:HAL:hal-00002979v1
Provided by: Hal-Diderot
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