Semigroup theory applied to options

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

Journal of Applied Mathematics, 2002, vol. 2, issue 3, 131-139

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.

Date: 2002
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https://doi.org/10.1155/S1110757X02111041

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2:y:2002:i:3:p:131-139

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