## Journal of Applied Mathematics

### Semigroup theory applied to options

#### 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 $C_0$-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

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

Dates
First available in Project Euclid: 30 March 2003

https://projecteuclid.org/euclid.jam/1049075016

Digital Object Identifier
doi:10.1155/S1110757X02111041

Mathematical Reviews number (MathSciNet)
MR1915662

Zentralblatt MATH identifier
1005.91059

#### Citation

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. https://projecteuclid.org/euclid.jam/1049075016

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