This paper studies some less known properties of the Black-Scholes equations and of its nonlinear modifications arising in Finance. In particular, the nonhypoellipticity of the linear Black-Scholes equation is shown; a comparison principle is formulated for a class of nonlinear degenerate parabolic equations which incorporates the most relevant financial applications; finally, some comments on the properties of the viscosity solutions are given. DOI: 10.1016/J.nonrwa.2010.10.003
Nonhypoellipticity and comparison principle for partial differential equations of Black-Scholes type
AGLIARDI, ROSSELLA;
2011
Abstract
This paper studies some less known properties of the Black-Scholes equations and of its nonlinear modifications arising in Finance. In particular, the nonhypoellipticity of the linear Black-Scholes equation is shown; a comparison principle is formulated for a class of nonlinear degenerate parabolic equations which incorporates the most relevant financial applications; finally, some comments on the properties of the viscosity solutions are given. DOI: 10.1016/J.nonrwa.2010.10.003File in questo prodotto:
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