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Solution to a nonlinear Black-Scholes equation

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Author(s): Maria Cristina Mariani | Emmanuel Kengni Ncheuguim | Indranil SenGupta

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2011;
Issue: 158,;
Start page: 1;
Date: 2011;
Original page

Keywords: Option pricing | Black-Scholes equation | Sobolev space | Schaefer's fixed point theorem

ABSTRACT
Option pricing with transaction costs leads to a nonlinear Black-Scholes type equation where the nonlinear term reflects the presence of transaction costs. Under suitable conditions, we prove the existence of weak solutions in a bounded domain and we extend the results to the whole domain using a diagonal process.
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