Arrow-Debreu model

Arrow-Debreu is most commonly used nowadays in financial economics with reference to Arrow-Debreu security. A canonical Arrow Debreu security is a security that pays one if a particular state of the world is reached and zero otherwise. As such, any derivatives contract whose settlement value is a function on an underlying whose value is uncertain at contract date can be decomposed as linear combination of Arrow-Debreu securities.

The concept of Arrow-Debreu security is a very nice pedagogical tool to understand pricing and hedging issues in derivatives analysis.It's practical use however in financial engineering has turned out to be very limited, especially in the multi-period or continuous markets.

The Black Scholes analysis and its extensions, despite their strong questionable assumptions have proven more successful in practice and has led to explosion of the derivatives industry.

An emerging concept has now appeared, called BICs, extending and generalizing arrow-debreu security as well as synthesizing the Black Scholes analysis in a multi-period markets while being practically very tractable.