A non-linear Black-Scholes equation. (2nd June 2009)

• Record Type: Journal Article
• Authors: Qiu, Yan; Lorenz, Jens
• Is Part Of: International journal of business performance and supply chain modelling. Volume 1:Number 1(2009)
• Page Start: 33
• Page End: 40
• Publication Date: 2009-06-02
• Subjects: Black-Scholes equation -- uncertain volatility -- nonlinear partial differential equations -- Cauchy problem -- nonlinear PDE -- options pricing; Business logistics -- Research -- Periodicals; 658.5005
• Languages: English
• ISSNs: 1758-9401

Abstract

We study a modification of the Black-Scholes equation allowing for uncertain volatility. The model leads to a partial differential equation with non-linear dependence upon the highest derivative. Under certain assumptions, we show existence and uniqueness of a solution to the Cauchy problem.