Small time path behavior of double stochastic integrals and applications to stochastic control
| dc.creator | Cheridito, Patrick | |
| dc.creator | Soner, H. Mete | |
| dc.creator | Touzi, Nizar | |
| dc.date | 2006-02-21 | |
| dc.date.accessioned | 2026-07-07T07:03:38Z | |
| dc.date.available | 2026-07-07T07:03:38Z | |
| dc.description | We study the small time path behavior of double stochastic integrals of the form $\int_0^t(\int_0^rb(u) dW(u))^T dW(r)$, where $W$ is a $d$-dimensional Brownian motion and $b$ is an integrable progressively measurable stochastic process taking values in the set of $d\times d$-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. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051605000000557 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0602453 | |
| dc.identifier | http://arxiv.org/abs/math/0602453 | |
| dc.identifier | Annals of Applied Probability 2005, Vol. 15, No. 4, 2472-2495 | |
| dc.identifier | doi:10.1214/105051605000000557 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109047 | |
| dc.subject | Probability | |
| dc.subject | 60G17, 60H05, 60H30, 91B28 (Primary) | |
| dc.title | Small time path behavior of double stochastic integrals and applications to stochastic control | |
| dc.type | text |