Nonhypoellipticity and comparison principle for partial differential equations of Black-Scholes type

none3This 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.2010.10.003Impact factor: 2.381mixedAgliardi R.; Popivanov P.; Slavova A.Agliardi R.; Popivanov P.; Slavova A