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On the pathwise large deviations of stochatic differential and functional differential equations with applications to finance

Wu, Huizhong (2009) On the pathwise large deviations of stochatic differential and functional differential equations with applications to finance. PhD thesis, Dublin City University.

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Abstract

The thesis deals with the asymptotic behaviour of highly nonlinear stochastic differential equations, as well as linear and nonlinear functional differential equations. Both ordinary functional and neutral equations are analysed. In the first chapter, a class of nonlinear stochastic differential equations which satisfy the Law of the Iterated Logarithm is studied, and the results applied to a financial market model. Mainly scalar equations are considered in the first chapter. The second chapter deals with a more general class of finite-dimensional nonlinear SDEs and SFDEs, employing comparison and time change methods, as well as martingale inequalities, to determine the almost sure rate of growth of the running maximum of functionals of the solution. The third chapter examines the exact almost sure rate of growth of the large deviations for affine stochastic functional differential equations, and for equations with additive noise which are subject to relatively weak nonlinearities at infinity. The fourth chapter extends conventional conditons for existence and uniqueness of neutral functional differential equations to the stochastic case. The final chapter deals with large fluctuations of stochastic neutral functional differential equations.

Item Type:Thesis (PhD)
Date of Award:November 2009
Refereed:No
Supervisor(s):Appleby, John
Subjects:Business > Finance
Mathematics > Differential equations
Mathematics
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
Funders:Science Foundation Ireland, School of Mathematical Sciences, DCU
ID Code:14870
Deposited On:12 Nov 2009 16:25 by John Appleby. Last Modified 12 Nov 2009 16:25

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