Post-crisis macrofinancial modeling: continuous time approaches

Prior to the crisis the dominant paradigm in macroeconomic modeling was the micro-founded "New-Keynesian" DSGE model (described in many textbooks including the influential exposition of Woodford (2003)). In its most basic form this combines price-stickiness with forward looking decision making by both households and firms. This provides a tractable framework for capturing the response of output and inflation to both demand and supply shocks and explaining intuitively the transmission of monetary policy (with monetary policy characterized as a choice over rules for current and future interest rates).