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• W2214458672 abstract "OF THE DISSERTATION Degenerate Partial Differential Equations and Applications to Probability Theory and Foundations of Mathematical Finance by Camelia Alexandra Pop Dissertation Director: Professor Paul M. N. Feehan In the first part of our thesis, we prove existence, uniqueness and regularity of solutions for a certain class of degenerate parabolic partial differential equations on the half space which are a generalization of the Heston operator. We use these results to show that the martingale problem associated with the differential operator is well-posed and we build generalized Heston-like processes which match the one-dimensional probability distributions of a certain class of Ito processes. The second part of our thesis is concerned with the study of regularity of solutions to the variational equation associated to the elliptic Heston operator. With the aid of weighted Sobolev spaces, we prove supremum bounds, a Harnack inequality, and Holder continuity near the boundary for solutions to elliptic variational equations defined by the Heston partial differential operator. Finally, we establish stochastic representations of solutions to elliptic and parabolic boundary value problems and obstacle problems associated to the Heston generator. In mathematical finance, solutions to parabolic obstacle problems correspond to value functions for American-style options." @default.
• W2214458672 created "2016-06-24" @default.
• W2214458672 creator A5072070403 @default.
• W2214458672 date "2012-01-01" @default.
• W2214458672 modified "2023-09-23" @default.
• W2214458672 title "DEGENERATE PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS TO PROBABILITY THEORY AND FOUNDATIONS OF MATHEMATICAL FINANCE" @default.
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• W2214458672 doi "https://doi.org/10.7282/t30k27hb" @default.
• W2214458672 hasPublicationYear "2012" @default.
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