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...

This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and electricity. Uniqueness of polynomial...

Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While Collin-Dufresne and Goldstein (2002) showed that no two-factor Cox-Ingersoll-Ross (CIR) model can...