Journal of Mathematical Finance, 2017, 7, 934-940 http://www.scirp.org/journal/jmf ISSN Online: 2162-2442 ISSN Print: 2162-2434 DOI: 10.4236/jmf.2017.74051 Nov. 28, 2017 934 Journal of Mathematical Finance On the Inverse Problem of Dupire’s Equation with Nonlocal Boundary and Integral Conditions Coskun Guler 1 , Volkan Oban 2 1 Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey 2 Department of Mathematical Engineering, Istanbul Technical University, Istanbul, Turkey Abstract In this study, Inverse Problem for Dupire’s Equation with nonlocal boundary and integral conditions is studied. Then, by means of the some transforma- tion, this equation is converted to diffusion equation. The conditions for the existence and uniqueness of a classical solution of the problem under consid- eration are established and continuous dependence of ( ) , v ρ on the data is shown. It is emphasized that this problem is well-posed. Keywords Mathematical Finance, Dupire’s Formula, Dupire’s Equation, Local Volatility, Diffusion Equation, Inverse Problem, Well-Posedness 1. Introduction In mathematical finance, Dupire’s formula (local volatility) is expressed in the following form ( ) 2 2 1 , 2 V V rS t S St S V S σ ∂ ∂ + ∂ ∂ = ∂ ∂ The Dupire formula enables us to deduce the volatility function in a local vo- latility model from quoted put and call options in the market. In a local volatility model the asset price model is under a risk-neutral measurement. For the rele- vant formula, reference [1]. Non-homogeneous Dupire’s equation is shown as follows, How to cite this paper: Guler, C. and Oban, V. (2017) On the Inverse Problem of Dupire’s Equation with Nonlocal Boundary and Integral Conditions. Journal of Ma- thematical Finance, 7, 934-940. https://doi.org/10.4236/jmf.2017.74051 Received: October 11, 2017 Accepted: November 25, 2017 Published: November 28, 2017 Copyright © 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access