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

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