Solution to a nonlinear Black-Scholes equation
- Resource Type
- article
- Authors
- Maria Cristina Mariani; Emmanuel Kengni Ncheuguim; Indranil SenGupta
- Source
- Electronic Journal of Differential Equations, Vol 2011, Iss 158,, Pp 1-10 (2011)
- Subject
- Option pricing
Black-Scholes equation
Sobolev space
Schaefer's fixed point theorem
Mathematics
QA1-939
- Language
- English
- ISSN
- 1072-6691
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.