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On the Inverse Problem of Dupire’s Equation with Nonlocal Boundary and Integral Conditions
Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
Department of Mathematical Engineering, Istanbul Technical University, Istanbul, Turkey
- 1 Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
- 2 Department of Mathematical Engineering, Istanbul Technical University, Istanbul, Turkey
Journal of Mathematical Finance·Volume 07 (2017)·Pages 934–940·Published 29 September 2017·DOI10.4236/jmf.2017.74051
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Abstract
In this study, Inverse Problem for Dupire’s Equation with nonlocal boundary and integral conditions is studied. Then, by means of the some transformation, this equation is converted to diffusion equation. The conditions for the existence and uniqueness of a classical solution of the problem under consideration are established and continuous dependence of ( p , v ) on the data is shown. It is emphasized that this problem is well-posed.
KeywordsMathematical FinanceDupire’s FormulaDupire’s EquationLocal VolatilityDiffusion EquationInverse ProblemWell-Posedness
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