Electron. J. Diff. Eqns., Vol. 2009(2009), No. 91, pp. 1-17.

Distribution-valued weak solutions to a parabolic problem arising in financial mathematics

Michael Eydenberg, Maria Cristina Mariani

Abstract:
We study distribution-valued solutions to a parabolic problem that arises from a model of the Black-Scholes equation in option pricing. We give a minor generalization of known existence and uniqueness results for solutions in bounded domains $\Omega \subset \mathbb{R}^{n+1}$ to give existence of solutions for certain classes of distributions $f\in \mathcal{D}'(\Omega)$. We also study growth conditions for smooth solutions of certain parabolic equations on $\mathbb{R}^n\times (0,T)$ that have initial values in the space of distributions.

Submitted September 10, 2008. Published July 30, 2009.
Math Subject Classifications: 35K10, 35D30, 91B28.
Key Words: Weak solutions; parabolic differential equations; Black-Scholes type equations.

Show me the PDF file (298 KB), TEX file, and other files for this article.

  Michael Eydenberg
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003-8001, USA
email: mseyden@nmsu.edu
María Cristina Mariani
Department of Mathematical Sciences
University of Texas, El Paso, Bell Hall 124
El Paso, Texas 79968-0514, USA
email: mcmariani@utep.edu

Return to the EJDE web page