Hein, Torsten : L^2-estimates of weak solutions of parabolic Cauchy problems and their application to the option pricing problem

Author(s):

Hein, Torsten

Title:

L^2-estimates of weak solutions of parabolic Cauchy problems and their application to the option pricing problem

Electronic source:

application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 5, 2004

Mathematics Subject Classification:

35B45			[ A priori estimates ]
35K10			[ General theory of second-order, parabolic equations ]
91B24			[ Price theory and market structure ]

Abstract:

This paper deals with L^2-estimates for weak solutions of one-dimensional parabolic Cauchy problems. These results were applied to the option pricing problem that arises in the Black-Scholes framework. In particular the continuous dependence of option prices from the underlying volatility and the Fréchet differentiatility are examined in specific spaces.

Keywords:

parabolic equation, Cauchy problem, weak solution, L^2-estimates, Black-Scholes equation, option pricing

Language:

English

Publication time:

4 / 2004