Maria Cristina Mariani, Emmanuel K. Ncheuguim, Indranil SenGupta
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.
Submitted August 20, 2010. Published November 28, 2011.
Math Subject Classifications: 91G80, 35B45, 58J35, 35D30.
Key Words: Option pricing; Black-Scholes equation; Sobolev space;
Schaefer's fixed point theorem.
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Maria Cristina Mariani Department of Mathematical Sciences The University of Texas at El Paso, Bell Hall 124 El Paso, TX 79968-0514, USA email: mcmariani@utep.edu |
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Emmanuel Kengni Ncheuguim Department of Mathematical Sciences New Mexico State University Las Cruces, NM 88003-8001, USA email: emmanou@nmsu.edu |
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Indranil SenGupta Department of Mathematical Sciences The University of Texas at El Paso, Bell Hall 124 El Paso, TX 79968-0514, USA email: isengupta@utep.edu |
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