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18 June 2002 Semigroup theory applied to options
D. I. Cruz-Báez, J. M. González-Rodríguez
J. Appl. Math. 2(3): 131-139 (18 June 2002). DOI: 10.1155/S1110757X02111041


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.


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D. I. Cruz-Báez. J. M. González-Rodríguez. "Semigroup theory applied to options." J. Appl. Math. 2 (3) 131 - 139, 18 June 2002.


Published: 18 June 2002
First available in Project Euclid: 30 March 2003

zbMATH: 1005.91059
MathSciNet: MR1915662
Digital Object Identifier: 10.1155/S1110757X02111041

Primary: 35K15 , 44A15
Secondary: 47D06 , 91B28

Rights: Copyright © 2002 Hindawi


Vol.2 • No. 3 • 18 June 2002
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