The Annals of Applied Probability

Small time path behavior of double stochastic integrals and applications to stochastic control

Patrick Cheridito, H. Mete Soner, and Nizar Touzi

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Abstract

We study the small time path behavior of double stochastic integrals of the form 0t(0rb(u) dW(u))TdW(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.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 4 (2005), 2472-2495.

Dates
First available in Project Euclid: 7 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1133965769

Digital Object Identifier
doi:10.1214/105051605000000557

Mathematical Reviews number (MathSciNet)
MR2187301

Zentralblatt MATH identifier
1099.60027

Subjects
Primary: 60G17: Sample path properties 60H05: Stochastic integrals 60H30: Applications of stochastic analysis (to PDE, etc.) 91B28

Keywords
Double stochastic integrals law of the iterated logarithm stochastic control hedging under gamma constraints

Citation

Cheridito, Patrick; Soner, H. Mete; Touzi, Nizar. Small time path behavior of double stochastic integrals and applications to stochastic control. Ann. Appl. Probab. 15 (2005), no. 4, 2472--2495. doi:10.1214/105051605000000557. https://projecteuclid.org/euclid.aoap/1133965769


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References

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