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

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Cheridito, P.
Touzi, N.

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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 constraints.

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Institute of Mathematical Statistics (IMS)

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Mathematics, Statistics and probability

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Annals of Applied Probability

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10.1214/105051605000000557

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