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Stochastic Integrals and Conditional Full Support

Part of: Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Mikko S. Pakkanen
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.

Keywords

Conditional full supportstochastic integralstochastic volatilitystochastic differential equation

MSC classification

Secondary: 60H05: Stochastic integrals
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 650 - 667
Copyright
Copyright © Applied Probability Trust 2010 

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