Generalized Arrow Pricing to Understand Financial Markets

Summary Most of the concepts that are used in modern theory of financial markets are contained in a paper published by Arrow in 1953. Arrow's model generalizes to non finite set of states describing uncertainty so as to encompass general financial assets pricing. We present several theorems of equivalence between General Equilibrium and Perfect Foresight Equilibrium (PFE), a concept adapted to financial assets markets. These results put forward several points: -The welfare properties of PFE, or in Arrow's term, the "role of securities in the optimal allocation of risk". -The role of the complete market hypothesis (CMS) and the reason why it takes an abstract mathematical form in modern finance. -The probabilistic interpretation of assets prices under the CMS hypothesis. This interpretation extends to dynamic models (as the equivalent martingale property) and allows the pricing of assets by their expected payments. -The necessary properties of equilibrium prices which are well defined by a linear, positive, continuous form. These properties are equivalent to three "no arbitrage" conditions that can be found in finance models without reference to equilibrium