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

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

Dublin City University

Year dc:date.issued

2009

Author dc:creator

• Wu, Huizhong

• Finance
• Differential equations
• Mathematics

Language dc:language

en