1. SEMIGROUP THEORY APPLIED TO OPTIONS.
- Author
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CRUZ-BÁEZ, D. I. and GONZÁLEZ-RODRÍGUEZ, J. M.
- Subjects
- *
OPTIONS (Finance) , *MATHEMATICAL functions , *ASSETS (Accounting) , *CAPITAL , *SEMIGROUPS (Algebra) - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2009