Abstract
We study the small time path behavior of double stochastic integrals of the form f 0 t (f 0 r b(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.
Original language | English (US) |
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Pages (from-to) | 2472-2495 |
Number of pages | 24 |
Journal | Annals of Applied Probability |
Volume | 15 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2005 |
Keywords
- Double stochastic integrals
- Hedging under gamma constraints
- Law of the iterated logarithm
- Stochastic con-trol
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty