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

Pages: 91 - 101, Issue Special, September 2011

 Abstract        Full Text (336.6K)              

John A. D. Appleby - Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland (email)
John A. Daniels - Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland (email)

Abstract: We consider an ane 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.

Keywords:  Volterra equation, stochastic functional di erential equation, admissibility, Volterra operator, con uent hypergeometric function, inecient market.
Mathematics Subject Classification:  Primary: 34K12, 34K50, 45D05, 45A05, 45J05, 45M05, 34E05, 33C15, 91B25, 91B69, 91B70; Secondary: 34K06, 60H20, 47G10, 91B26, 91G80.

Received: July 2010;      Revised: June 2011;      Published: October 2011.