A non-linear Black-Scholes equation

Yan Qiu and Jens Lorenz

International Journal of Business Performance and Supply Chain Modelling, 2009, vol. 1, issue 1, 33-40

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. (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:ids:ijbpsc:v:1:y:2009:i:1:p:33-40

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