Journal of Applied Mathematics

Semigroup theory applied to options

D. I. Cruz-Báez and J. M. González-Rodríguez

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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.

Article information

J. Appl. Math., Volume 2, Number 3 (2002), 131-139.

First available in Project Euclid: 30 March 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K15: Initial value problems for second-order parabolic equations 44A15: Special transforms (Legendre, Hilbert, etc.)
Secondary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 91B28


Cruz-Báez, D. I.; González-Rodríguez, J. M. Semigroup theory applied to options. J. Appl. Math. 2 (2002), no. 3, 131--139. doi:10.1155/S1110757X02111041.

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