Open AccessA non-linear Black-Scholes equation
Author(s) -
Yan Qiu,
Jens Lorenz
Publication year - 2009
Publication title -
international journal of business performance and supply chain modelling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.243
H-Index - 15
eISSN - 1758-941X
pISSN - 1758-9401
DOI - 10.1504/ijbpscm.2009.026264
Subject(s) - uniqueness , black–scholes model , mathematics , volatility (finance) , partial differential equation , derivative (finance) , mathematical analysis , econometrics , economics , financial economics
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.
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