Consumption, Growth and Asset Pricing: A Regime Switching and Robust Control

We extends the aggregate risk modeling approach to include the regime switching risk triggered by a `regime shift' in economic conditions and to uncertainty aversion (robust control). We use a regime switching process rather than the popular diffusion-jump process for a number of reasons. Firstly, regime switching processes are better suited to analyzing economic business cycles than is the diffusion-jump process. Secondly, in a regime switching process, the (drift and diffusion) parameters of the stochastic process are regime specific. Finally, the regime switching process captures the fact that risk premia seem to be higher at business cycle troughs than they are at peaks. As for the robust control feature of the model, we adopt a kappa-ignorance framework, which is a special case of the recursive multiple-priors model. This framework results in a portfolio rule which is observationally equivalent to an effective decrease in the mean of wealth (risky asset). The clear advantage of using the robust control approach is that the portfolio rule gives rise to the risk premium due to ``first-order risk aversion'' since the risk premium is proportional to the instantaneous standard deviation of the aggregate state variable. With these two features, the framework will be better suited to analyze consumption, growth and asset pricing issues.