Title: A non-linear Black-Scholes equation

Authors: Yan Qiu, Jens Lorenz

Addresses: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA. ' Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA

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.

Keywords: Black-Scholes equation; uncertain volatility; nonlinear partial differential equations; Cauchy problem; nonlinear PDE; options pricing.

DOI: 10.1504/IJBPSCM.2009.026264

International Journal of Business Performance and Supply Chain Modelling, 2009 Vol.1 No.1, pp.33 - 40

Published online: 31 May 2009 *

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