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

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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

John A. D. Appleby ^1, and John A. Daniels ^1,

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

Abstract
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We consider an ane stochastic dierential 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 dierential equation, and show that the solution of the equation has the same asymptotic rate of growth, almost surely.

Keywords: admissibility, stochastic functional dierential equation, con uent hypergeometric function, inecient market., Volterra equation, Volterra operator.

Mathematics Subject Classification: Primary: 34K12, 34K50, 45D05, 45A05, 45J05, 45M05, 34E05, 33C15, 91B25, 91B69, 91B70; Secondary: 34K06, 60H20, 47G10, 91B26, 91G8.

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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