dc.contributor.advisor Knessl, Charles en_US dc.contributor.author Xu, Miao en_US dc.date.accessioned 2012-12-07T11:56:02Z dc.date.available 2012-12-07T11:56:02Z dc.date.available 2014-04-15T09:30:39Z dc.date.created 2011-08 en_US dc.date.issued 2012-12-07 dc.date.submitted 2011-08 en_US dc.identifier.uri http://hdl.handle.net/10027/8921 dc.description.abstract We consider an American put option under the Constant Elasticity of Variance (CEV) process. This corresponds to a free boundary problem for a partial differential equation (PDE). We show that this free boundary satisfies a nonlinear integral equation, and analyze it in the limit of small $\rho$ = $2r/ \sigma^2$, where $r$ is the interest rate and $\sigma$ is the volatility. We find that the free boundary behaves differently for five ranges of time to expiry. We then analyze option price $P(S,t)$, as a function of the asset price $S$ and time to expiry $t$. We obtain the asymptotic expansion of $P$ as $\rho \rightarrow 0$, first via an integral equation formulation, and then using the PDE satisfied by $P$, and analyzing it by perturbation theory and matched asymptotic expansions. en_US dc.language.iso en en_US dc.rights Copyright 2011 Miao Xu dc.subject Asymptotic Methods en_US dc.subject Partial Differential Equations en_US dc.subject Mathematical Finance en_US dc.subject Analysis en_US dc.title Asymptotic Methods applied to an American Option under a CEV Process en_US thesis.degree.department Mathematics, Statistics, and Computer Science en_US thesis.degree.discipline Applied Mathematics en_US thesis.degree.grantor University of Illinois at Chicago en_US thesis.degree.level Doctoral en_US thesis.degree.name PhD, Doctor of Philosophy en_US dc.type.genre thesis en_US dc.contributor.committeeMember Nicholls, David en_US dc.contributor.committeeMember Yang, Jie en_US dc.contributor.committeeMember Abramov, Rafael en_US dc.contributor.committeeMember Sclove, Stanley en_US dc.type.material text en_US
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