Portfolio Rules and Interest Rates under Model Uncertainty

This paper incorporates model uncertainty to study an inter-temporal investment-consumption choice problem. Using a modified Cox-Ingersoll-Ross model in a complete market context, we propose an approach for quantifying uncertainty, which requires only an uncertainty parameter rather than an uncertainty process and provides closed-form solutions that are time-consistent under commitment. We also derive closed-form equilibrium solutions to study both the interest rate and the market price of risk. Calibrations show that the impact of model uncertainty could be enormous, lowering the equilibrium risk-free rate and increasing the equity risk premium. This finding contributes to a potential explanation for the equity risk premium and risk-free rate puzzles. Different from earlier literature, our calibrations suggest substantial model mis-specification uncertainty is necessary to explain the equity risk premium puzzle. In this paper, the equilibrium wealth and expected utility under model uncertainty are also studied