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

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.

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  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

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