# American Institute of Mathematical Sciences

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2011, 2011(Special): 91-101. doi: 10.3934/proc.2011.2011.91

## Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles

 1 Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland, Ireland

Received  July 2010 Revised  June 2011 Published  October 2011

We consider an ane stochastic di erential equation with an av- erage functional. In our main results, we determine the asymptotic rate of growth of the mean of the solution of this functional di erential equation, and show that the solution of the equation has the same asymptotic rate of growth, almost surely.
Citation: John A. D. Appleby, John A. Daniels. Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles. Conference Publications, 2011, 2011 (Special) : 91-101. doi: 10.3934/proc.2011.2011.91
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