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dc.contributor.authorQiu, Yan
dc.date.accessioned2010-09-09T22:09:30Z
dc.date.available2010-09-09T22:09:30Z
dc.date.issued2010-09-09
dc.date.submittedJuly 2010
dc.identifier.urihttp://hdl.handle.net/1928/11130
dc.description.abstractThe Black Scholes equation is a fundamental model for derivative pricing. Modifying its assumptions will lead to more realistic but mathematically more complicated models. This dissertation consists of analytical and numerical studies about one particular type of nonlinear Black Scholes models, whose nonlinearity lies in the highest spatial derivative 1 with discontinuous coefficient function. First we smooth out the discontinuous term and focus only on the nonlinearity. We consider the case where the volatility is a smooth function and present some basic existence and uniqueness results. To study the discontinuity we simplify the problem by discretizing the Partial Differential Equation PDE only in time and consider the evolution in a given tiny time step from initial data. We perform convergence and perturbation analysis to the Ordinary Differential Equation (ODE) with discontinuous coefficient and obtain some insight of how the curves, where the discontinuity occurs, evolve in the space-time plane for the PDE. Last we obtain numerical results for the nonlinear PDE in the setting of a moving boundary problem.en_US
dc.language.isoen_USen_US
dc.subjectBlack Scholes Modelen_US
dc.subjectNonlinear PDEen_US
dc.subjectMoving Boundary Problemen_US
dc.subject.lcshDerivative securities--Prices--Mathematical models.
dc.subject.lcshNonlinear partial differential operators.
dc.titleAnalysis of nonlinear Black Scholes modelsen_US
dc.typeDissertationen_US
dc.description.degreeMathematicsen_US
dc.description.levelDoctoralen_US
dc.description.departmentUniversity of New Mexico. Dept. of Mathematics and Statisticsen_US
dc.description.advisorLorenz, Jens
dc.description.committee-memberEmbid, Pedro
dc.description.committee-memberSauer, Christine
dc.description.committee-memberPereyra, Cristina


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