On the theory of option pricing

The objective of this article is to provide an axiomatic framework in order to define the concept of value function for risky operations for which there is no market. There is a market for assets, whose prices are characterized as stochastic processes. The method consists of constructing a portfolio of these assets which will mimic the risks involved in the operation. We follow the terminology of the theory of options although the set-up goes beyond that particular problem.