Journal of Applied Mathematics

Journal of Applied Mathematics / 2002 / Article

Open Access

Volume 2 |Article ID 245081 | https://doi.org/10.1155/S1110757X02111041

D. I. Cruz-Báez, J. M. González-Rodríguez, "Semigroup theory applied to options", Journal of Applied Mathematics, vol. 2, Article ID 245081, 9 pages, 2002. https://doi.org/10.1155/S1110757X02111041

Semigroup theory applied to options

Received05 Nov 2001
Revised05 Mar 2002

Abstract

Black and Scholes (1973) proved that under certain assumptions about the market place, the value of a European option, as a function of the current value of the underlying asset and time, verifies a Cauchy problem. We give new conditions for the existence and uniqueness of the value of a European option by using semigroup theory. For this, we choose a suitable space that verifies some conditions, what allows us that the operator that appears in the Cauchy problem is the infinitesimal generator of a C0-semigroup T(t). Then we are able to guarantee the existence and uniqueness of the value of a European option and we also achieve an explicit expression of that value.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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