We study the small time path behavior of double stochastic integrals of the form ∫0t(∫0rb(u) dW(u))T dW(r), where W is a d-dimensional Brownian motion and b is an integrable progressively measurable stochastic process taking values in the set of d×d-matrices. We prove a law of the iterated logarithm that holds for all bounded progressively measurable b and give additional results under continuity assumptions on b. As an application, we discuss a stochastic control problem that arises in the study of the super-replication of a contingent claim under gamma constraints.
Publié le : 2005-11-14
Classification:
Double stochastic integrals,
law of the iterated logarithm,
stochastic control,
hedging under gamma constraints,
60G17,
60H05,
60H30,
91B28
@article{1133965769,
author = {Cheridito, Patrick and Soner, H. Mete and Touzi, Nizar},
title = {Small time path behavior of double stochastic integrals and applications to stochastic control},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 2472-2495},
language = {en},
url = {http://dml.mathdoc.fr/item/1133965769}
}
Cheridito, Patrick; Soner, H. Mete; Touzi, Nizar. Small time path behavior of double stochastic integrals and applications to stochastic control. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 2472-2495. http://gdmltest.u-ga.fr/item/1133965769/