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

✍ Scribed by R. Agliardi; P. Popivanov; A. Slavova

• Book ID: 104070259
• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 242 KB
• Volume: 12
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2010.10.003

✦ Synopsis

This paper studies some less known properties of the Black-Scholes equation 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.