Journal of Applied Probability

Stochastic integrals and conditional full support

Mikko S. Pakkanen

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We present conditions that imply the conditional full support (CFS) property, introduced in Guasoni, Rásonyi and Schachermayer (2008), for processes Z := H + ∫K dW, where W is a Brownian motion, H is a continuous process, and processes H and K are either progressive or independent of W. Moreover, in the latter case, under an additional assumption that K is of finite variation, we present conditions under which Z has CFS also when W is replaced with a general continuous process with CFS. As applications of these results, we show that several stochastic volatility models and the solutions of certain stochastic differential equations have CFS.

Article information

J. Appl. Probab. Volume 47, Number 3 (2010), 650-667.

First available in Project Euclid: 24 September 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91B28
Secondary: 60H05: Stochastic integrals

Conditional full support stochastic integral stochastic volatility stochastic differential equation


Pakkanen, Mikko S. Stochastic integrals and conditional full support. J. Appl. Probab. 47 (2010), no. 3, 650--667. doi:10.1239/jap/1285335401.

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