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Stochastic Integrals and Conditional Full Support

Published online by Cambridge University Press:  14 July 2016

Mikko S. Pakkanen*
Affiliation:
University of Helsinki
*
Postal address: Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FI-00014 Helsingin yliopisto, Finland. Email address: msp@iki.fi
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Abstract

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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.

MSC classification

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2010 

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