Introduction to a theory of value coherent with the no arbitrage principle

This paper defines the Value of a general claim based on agent's preferences and coherent with the No Arbitrage Principle. This Value is a non trivial extension of the certainty equivalent since it takes into consideration the possibility of partially hedging the risk carried by the claim. When the market is complete this Value is the unique no arbitrage price. When the risk may not even be partially covered, this Value is the certainty equivalent. Between these two cases just some of the risk may be hedged and the no arbitrage principle requires the price to lie in the "arbitrage interval". The Value we propose is exactly designed to satisfy this condition.