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 R.; Popivanov P.; Slavova A.. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - STAMPA. - 12:3(2011), pp. 1429-1436. [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.2010.10.003I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
