IJPAM: Volume 76, No. 2 (2012)
OF A -SEMIGROUP AND APPLICATIONS
Department of Applied Mathematics and Systems
Artificios, 40, México, D.F. 01120, MEXICO
Abstract. Considering the Black-Scholes equation as a Cauchy problem for different options: european, asian and vanilla, in this work we see that the second order differential operator
on the Schwartz space , generates a -semigroup. We also find the corresponding solution as some class of evolution equation.
Received: August 24, 2011
AMS Subject Classification: 47D06, 47D60, 91G80
Key Words and Phrases: black-scholes equation, differential operator, -semigroups, Vanilla option, Asian option.
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395