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
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 -semigroup . 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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