Inverse Problems and Its Applications in Financial Problems
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Abstract
Inverse problems could be described as the relationship between system inputs and outputs. In general, a solution obtained from numerical solving for an inverse problem is said to be unstable. So the inverse problems can be ill-posed problems according to the Hadamand’s criteria. By relaxing the process of solving the problem with the corresponding regularization theorem, the stability of the solution will be obtained. In this review article, the mathematical analysis for solving inverse problems and a comprehensive account of regularization theorem are presented. Finally, we show some examples for solving local volatility in financial derivatives which is deemed an important aspect of inverse problems concerning the field of applied mathematics for finance.
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References
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