Abstract
The Fichera theory was first proposed in 1960 by Gaetano Fichera and later developed by Olejnik and Radkevič in 1973. It turned out to be very useful for establishing the well-posedness of initial boundary value problems for parabolic partial differential equations degenerating to hyperbolic ones at the boundary.
In this paper we outline the application of the Fichera theory to interest rates models of Cox-Ingersoll-Ross (CIR) and Chan-Karolyi-Longstaff-Sanders (CKLS) type. For the one-factor CIR model the obtained results are consistent with the corresponding Feller condition.
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References
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Acknowledgements
The authors were partially supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE—Novel Methods in Computational Finance) and by the bilateral German-Slovakian Project NL-BS—Numerical Solution of Nonlinear Black-Scholes Equations, financed by the DAAD (01/2013-12/2014).
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Bučková, Z., Ehrhardt, M., Günther, M. (2016). Fichera Theory and Its Application in Finance. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. ECMI 2014. Mathematics in Industry(), vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-23413-7_13
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DOI: https://doi.org/10.1007/978-3-319-23413-7_13
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