Small time path behavior of double stochastic integrals and applications to stochastic control
Open Access
- 1 November 2005
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 15 (4) , 2472-2495
- https://doi.org/10.1214/105051605000000557
Abstract
We study the small time path behavior of double stochastic integrals of othe form f(0)(t)(f(0)(r) b(u) dW(u))(T) dW(r), where W is ad-dimensional Brownian motion and b is an integrable progressively measurable stochastic process taking values in the set of d x 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 constraintsKeywords
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This publication has 7 references indexed in Scilit:
- The multi-dimensional super-replication problem under gamma constraintsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 2005
- Hedging and Portfolio Optimization in Financial Markets with a Large TraderMathematical Finance, 2003
- Dynamic programming for stochastic target problems and geometric flowsJournal of the European Mathematical Society, 2002
- Stochastic Target Problems, Dynamic Programming, and Viscosity SolutionsSIAM Journal on Control and Optimization, 2002
- Superreplication Under Gamma ConstraintsSIAM Journal on Control and Optimization, 2000
- Continuous Martingales and Brownian MotionPublished by Springer Nature ,1999
- On the possibility of hedging options in the presence of transaction costsThe Annals of Applied Probability, 1997