Dimensionality Reduction by Fuzzy Transforms with Applications to Mathematical Finance

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F18%3AA1901TVX" target="_blank" >RIV/61988987:17610/18:A1901TVX - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-73150-6_19" target="_blank" >http://dx.doi.org/10.1007/978-3-319-73150-6_19</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-73150-6_19" target="_blank" >10.1007/978-3-319-73150-6_19</a>

Result language
angličtina
Original language name
Dimensionality Reduction by Fuzzy Transforms with Applications to Mathematical Finance
Original language description
Two distinguished properties of the F-transform: the best approximation in a local sense and the reduction in dimension imply the fact that the F-transform has many successful applications. We show that the technique of F-transform fully agrees with the technique of dimensionality reduction, based on Laplacian eigenmaps. To justify this claim, we characterize the processed by the F-transform data in terms of the adjacency graph that reflects their (data) intrinsic geometry. In the second part, we give an overview of the F-transform applications to mathematical finance: we discussed the estimation of market volatility and the numerical scheme and solution to the one-factor Black-Scholes partial differential equation.
Czech name
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Czech description
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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