Maturity randomization for stochastic control problems

Bouchard, Bruno; Karoui, Nicole El; Touzi, Nizar

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

Number

Publisher

Institute of Mathematical Statistics

Pages

2575-2605

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