Consider a d-dimensional Brownian motion X (Xl, ... ,Xd ) and a function F which belongs locally to the Sobolev space W 1,2. We prove an extension of Ito's formula where the usual second order terms are replaced by the quadratic covariations [fk(X), Xkj involving the weak first partial...

Using a standard frictionless, continuous time, and continuous trading stochastic economy with heterogeneous beliefs, the purpose of this paper is to provide sufficient conditions for the existence of competitive equilibrium in an incomplete asset market. A new approach to proving existence is...

This paper studies the relation between concavity, stochastic or state dependent utility functions, and risk aversion. Using the common definition of risk aversion, but modified for state dependent preferences, we show that concavity does not imply risk aversion. Instead, it implies a weaker...